and part returned to my address on the blockchain. I don't know why this split happened; but the fact is that I can't move the BTC that were stuck in my address because neither the exchange can transfer them anymore (as they have already left there)
Seems confuzing.
OmegaStarScream is correct. It must be a simple change address.
What you write above is strange... So, you say that "part returned to your address", but at the same time you say "the exchange can't transfer anymore as they've already left.
Assuming you had X btc in the exchange. Did you send all X to the hardware wallet?
If not, how much did you send? 50%, 70%, 10%?
If you sent 50%, does the exchange now have the rest 50%? If you sent 70% does the exchange now have 30%?