Is it permissible for me to push a cat away if it passes in front of me while I am praying? If I leave it, will I incur a sin?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

If a cat or whatsoever passes before you during the prayer from behind the sutrah, if you use any, then leave it, because the sutrah stands between you and the cat. If it passes between you and the sutrah or passes closely before you in case there is no sutrah and you are not in the standing position, then push it away as much as you can. Your prayer is valid regardless of whether it goes away or not. If it passes before you while you are standing in the prayer, then push it with your foot if you can. You should never lean over while you are standing to push it away in order for your prayer not to be invalid. Some scholars said that if the person leans down while standing in the prayer to pick a stone to kill a scorpion or so on, his prayer will be invalid because standing in the prayer is one of its pillar and leaning over diminishes its perfection.

Allah knows best.