Some previous answers might be worth exploring: u/poob1x has a detailed description of ancient contacts across the Bering Strait, and notes that the Yupik and Aleut peoples live on both sides of the strait. Here are some further answers from them about Asian contacts with North America. u/The_Alaskan describes some Medieval-era archaeological evidence of cross strait contacts.

For a closer, here is an answer I wrote about why Russia was actually very far away from the Bering Strait for much of history.