I was just wondering if there was ever a period in history, where the Ancient Romans had to do battle with armored knights or were they in two different time periods? Even if they were in two different time periods, did one side have any knowledge of the other?
Considering that the earliest "medieval knights" you could find would be Charlemagne in the late 700s/early 800s, and the non-Byzantine Roman Empire collapsed in the 400s, no.
Now, the Byzantine Empire ("Eastern Roman Empire, a splitoff from Italy-Rome that lasted until 1453) might very well have clashed with the other Europeans many times, and they were invaded in the 4th Crusade in 1202. But that's not legionnaires and tournament knights clashing in battle, which is probably what you were thinking of.
They were in two different periods. As such, they were unable to know about each other. I mean reciprocally. People who lived later (knights) did know (if interested) about those living earlier (ancient Romans), but obviously not vice versa.