Past And Future

Poul and Karen Anderson's The King Of Ys Tetralogy and Poul Anderson's The Last Viking Trilogy are set in different historical periods;

Poul Anderson's several future history series are set along alternative future timelines;

"Marius," the opening installment of Anderson's first future history series is named after the Roman general who defeats barbarian invaders in Anderson's The Golden Slave and who is also referenced in at least two other works by Anderson, the historical Ys and the futuristic Shield;

Anderson's main works on time travel and immortality cover past, present and future.

However, one thing that Anderson did not do was to link an entire series set in the past with another entire series set in a speculative future. The Terran Imperialists of his Technic History refer to the Roman Empire but not also to the Roman-era city-state of Ys, which, by decree of its departed deities, has been forgotten except as legend and fiction. An alternative version of Ys is mentioned in Anderson's The Broken Sword but that heroic fantasy is also set in our past. No time traveler visits both Ys and the Terran Empire. (Indeed, none visits either.) Jack Havig does visit both Constaninople and the period of the Maurai future history. However, he does all this in the course of a single novel.

It is unusual to link a past series to a future series but I know of two examples. Time travel links SM Stirling's Nantucket Trilogy to his Emberverse series and also links Julian May's Pliocene Exile Tetralogy to her Galactic Milieu Trilogy.

My advice: Read Anderson, Stirling and May.