Jameis Winston has been hit this preseason. A lot. And he came away from the third preseason game limping. The Tampa Bay Buccaneers initially wouldn't confirm that he was injured, but Dirk Koetter today said that Winston sprained his ankle against the Cleveland Browns.
Part of the problem is that Winston struggles to avoid hits in the pocket. He's pretty good at sliding and stepping out of bounds in the open field and he can move well in the pocket to avoid sacks, but he refuses to give up on plays in the pocket, which leads to him not going down until at least three defenders are piled on top of him. While none of those hits are particularly hard, just taking the sack early would make them a lot less taxing on his body -- and especially his ankles, as he's had defenders land on those at least twice this preseason.
It's not clear how serious Winston's ankle sprain is, but he said today that it's the "least of [his] worries." Quarterback's have frequently played through ankle sprains, and Winston noted that he'd done the same thing last year, but it tends to make them a lot less effective for rather obvious reasons. You need your ankles to plant and move, after all. The fact that Winston wasn't in a boot today and wasn't noted to have missed practice is probably a good indication that it really isn't all that serious, though.