Unfortunately at this point as the cat has bitten you it needs to be either quarantined or tested for rabies unless there is no rabies at all in your area.
If there is an animal control department in your town you need to call them or check with your police department about who handles animal bite situations.
I would keep the cats apart until you can work on getting him trapped and out of there.
Make sure there are cat boxes in both areas.
The two cats are likely to fight if they get together and you don't want that. So you might lock your cat in a bedroom or bathroom while you make sure the cat in the cellar area is set up for safe confinement.
If you have an animal control officer or a animal shelter they may be able to let you use a live trap to catch the cat.
Most cat germs have to be transmitted cat to cat but he could be leaving you fleas in your cellar so you might have to spray the room down there.
I'd clean and disinfect anything he uses for a catbox unless you use a box you can just throw away.
I understand you want to help this cat but you need to think about you and your pet's health in this situation.
Hope this helps you!
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