Mine Anastasiy-WWII( owned a ship building company during WWII), US western coast, Seattle. Aphrodite- greek goddess( ancient Greece) Baccus- same Byzantium- fan pet of the Byzantine empire Charming- based on a fairytale prince( from various fairytales, snow white, cinderella, etc..etc..), likely medieval setting Chryssa-present day, big city, likely New York City Constable- gold rush California Courante- muse, he's immortal so... no real actual time period Dowager- old woman, WWI love story... though she's old in the story and dying Geppetto- fairytale, no real imagined time period, likely set in Germany though. Huo- present day Shanghai Octantis- never really had a time period for her, to be honest. Roccoco- 18th century Paris( oops, wrong century...XD...corrected)
I left out most of the fan pets I have that are based off of artists, Titian, Waterhouse, Cassat, etc... as well as pets that I have that are not completely finished yet.
Also,
I have to say most of my pets lives, or in many cases died, in plain old present time xD, with a few exceptions: My doom and gloom couple (Doomsday and Gloom) happened to live before and through the Great Depression in Austria/London/California. Anarchist lives in year 2357...
Among unfinished pets: Ludwig is a tribute pet to Ludwig II of Bavaria, so that's mid to late 1800s. Viking will sure be somebody from the viking period. Johan is possibly going to be somebody lived in the mid 1700s.

Most of my pets/character's stories are set in present age, America so I'll just name those who arent set in the said time period.
Hagen - German "soldier" in WW II Arcanus - fantasy medieval-like world Luthien - medieval Europe Ming - medieval Asia Uno - my "Alien" OC who lives in the far future on LV-426 Reggie - post-apocalyptic world, America Cletus, Pius, Lucretius (and Paulus) - all set in ancient Roman. Originally I just planned on doing Cletus in this kind of setting because I am not very familar with this time period at all but since and me started this RP my Roman character number grew quite quickly x'D
I love topics like this one here, will for sure check back to read the replies.
Some guys from my account:
Haggard & Morpheus: Roman empire Cassius: 42BC Adam: 1910-1944 Suffer: 16th/17th century Prometheus: 19th century Spite: 1941 Valiant: first half of 20th century Nash: 24th century (Star Trek OC)
Oh goodness... All fake, but many of them are based on a real time period on planet Earth or aspects of legends and ancient mythologies.
Starting with my human historical AU characters: The world of Landry, Marceau, Haegan, Faryl, Lorkan, Galbraith, and Hooked is loosely based on (mostly fictional interpretations of) England during the 17th and 18th centuries with aspects of the Middle Ages thrown in in varying amounts, depending on the character. Escape is based on the Wild West and in my AU, the characters are contemporaries of those listed above. Salvatori's world is strongly inspired by the Prohibition era. The two characters in his story are not contemporaries of the other historical characters, and may not even exist in the same AU. I am undecided on the matter.
Moving on to my non-humans: Regnant and his Cohort are elves. Medieval times would probably be most applicable. Vaako, Sishean, Nalithar, and Aethril are all aliens... Their tech is advanced well beyond modern capabilities but there are aspects of their societies drawn from history. Sishean and Nalithar's world is superstitious and most people are highly misinformed thanks to the royal propaganda machine. Vaako's culture is like the Spartans in many aspects. Kink is a mix of modern and mythical with a touch of late 1800s-early 1900s explorer/adventurer thrown in. (Think: The Mummy, Indiana Jones, etc.) Classified represents a cyborg and an android. They live in futuristic post-devastation.
Cause is inspired by Arthurian legend, Curate is inspired by Shakespeare's plays and Tudor England, Immortals represents the Greek god Poseidon and his lover, Forsaken is inspired by Egyptian myth and ancient culture, and Invidious is inspired by Greco-Roman times. However, they all have broad-ranging timelines. In all cases, one or both characters they represent is long-lived and still alive in a fantasy version of modern times or the near future.
Characters whose stories takes place primarily in modern times, with only a little history thrown in: Hammered, Stature, Stockade, Ric, and Konnor (Possibly Divest as well.)
Last but not least are Rigr and Vidar... Their stories are tied in with Hammered, Stature, and Stockade but they are Norse gods (sorta) so obviously they have a bit more history. (Taking inspiration from Marvel comics here...) My version of Vidar has basically been living on Earth since Viking times and Rigr... Well, Rigr's more complicated. He's an alter ego of Heimdallr and he is not always around. Rigr doesn't really have any history beyond his history with Vidar, but of course Heimdallr himself has an extensive one so... Yeah. Like I said, it's complicated.
-stops and wipes brow- Okay. That's all of them... I think.
Most of mine are 15th-16th century, with one exclusion now of Arno who's French Revolution/latter half of the 18th century.

Ooh, French revolution, nice. :D
Very nice. I've tried setting pets in alternate versions of historical periods and couldn't really write it well so I commend someone who can. I think my mind has to wrap it in an actual historical setting for me to process it or something. It's also why I can't seem to create pets in completely fantastical settings for the most part unless it's someone immortal who just lives through different periods in general.
LOL I am always amazed when someone can actually be true to a particular time period, so I commend you for being able to do just that. I find it impossible to limit myself to reality, so all of my writing ends up having an element of fantasy. XD
Cold Snap, Heat Wave, Kayii, Dressmaker, Ruadhan, Faoladh, Kohala, Mingyu and Shuochang- Altered Modern Era (i.e. Supernatural/Fantasy stuff taking place in this day and age Tyrannical: 7th-8th Century Russia Patissere: Modern Era Alymere: He's sort of like Dr. Who, so he exists in all time periods but the one during his life and death. Obsolescent and Ameliorate: Steampunk Era/Victorian Era
Onley Salvador Dali lives in a specific time from 1904 until 1989. My other pets can tavel or be in eavery time. Mebe Valdus prefers to life in the 18th and 19th century. Rakizei kan for sure life in the future. But I believe the human in future can also time travel.
Oh I like these topics! It's always interesting to see.
Vadim and Josev are interesting as they're flexible. They died in the 1920s but exsit as ghosts even to this day.
Zakkier is set in a Dystopian Cyberpunk future, same as Hazen. Khristian is also based in the future, but he's post-apocalypse orientated. Snipers is an alternate timeline that exists as if the Cold War ended in nuclear strikes.
Stimpak is set in the Same universe as the Fallout video game series.
Arran and Magz are set in alternate modern day realities that involve the supernatural and such.
And the rest are pretty boring, haha.
I love topics like this. Most of my characters are set in modern day times, but I do have some exceptions.
My modern day characters are Aquamarine, Cher Ami, Dream Catcher (sort of) Kenji, Rained, Stripey, Kauta, Maiku, Pained, Eisen, Galixsia, Universte, Star King, Dappled, Jingles, Recillia, Silversy, Chadrick, Genu, Ikebana, Woundless (sort of), Highness, Pilot, Iridus, Shatter (sort of), Gungnir, Junipers, Ingeamia, and Kriena. The thing with Shatter and Woundless is that they're so freakishly old that they could easily appear in older eras. Shatter's character dates back to 4000 BC, and Woundless is around a thousand years old herself.
While I imagine Chadrick and Highness to live in modern times, their family and kingdom are still very traditional with their royalty system. So they're sort of in a modern day/medieval cross type of setting.
My medieval characters include Villanelle and Haikai. They were alive when the equivalent of the Salem Witch Trials were extremely common, and Villanelle herself was accused of being a witch. There's some fantasy aspects mixed into their world, since Haikai is (currently unknowingly) a witchling herself.
Ernte alone is in a steampunk era.
Dream Catcher alone would be considered an ancient day character. Dream Catcher is even older yet than both Shatter and Woundless. He dates back to nearly the beginning of the world that his character is in.
I have one more pet who's in foster right now, Zoisite. I imagine her character to have been born somewhere between medieval and modern times, which is unfortunately quite vague. She was raised by Shatter, and lives into modern times.
This is cool, weeee
Croi is based around 1200 BCE in the Celtic era Folaigh is as old as intelligent man and will remain until the end of man. Herbwife is based around the civil war and thereafter. Mehitabelle is my post-apocalypse alien babe in the 3050's Rosehips is like mmmm, 500 CE Solange and Ule are time travelers, and reside in whatever time period they are needed the most. Japeth and Dedrei are kind of I don't even know what I'm doing with them atm :(

All of my more solid-characters (Susurrous, Protector, Kindly and Enliven), are around the present time. Enliven's story is set more specifically to the year 2008, because that's the year I came up with it.
I don't know why I haven't set stories in different time periods...it might be that all the stories I make need to be in someway relatable to ME, in order for me to throw more into it (that's kinda lame, I know).
Might also be that I never feel knowledgeable enough to try a different time period...though thinking about it, I don't really know if I really need to be. : P
Maybe I could try it on a pet that I don't have a solid concept with yet. Though probably not Forested since his story doesn't really have a clear time-period because forests...well, they stay virtually the same unless the environment changes, so.
Polymath, Soliloquist and Organism do not have set stories yet, so we'll see.
That makes sense. I have characters set in present time, but most of them are not. In general, and this may be due to my history background I like setting characters in different times, it allows me to sort of write out stories other than my own and it exercises my random historical research urges.