Is it permissible to keep a sandal found in the mosque after one's original sandal was lost, given that there is a slight difference between the two?

If you ask those remaining in the mosque about the extra sandals in it, and only this one sandal remains, it is highly likely that its owner is the one who took your sandals. You may take it and keep it until you find your sandals or your suspicion changes. The scholars have mentioned that an oppressed person may take from the oppressor's wealth an amount equivalent to their right if they cannot find the exact item that is their right, based on the Almighty's saying: "And if you punish [an enemy], punish with an equivalent of that with which you were punished."