My mother is accusing me of taking checks from her that she has never received. How do I get her to understand that there are no checks?

This is unfortunately very common with dementia. If she hasn't been diagnosed, you need to get her to a doctor. Infections and medication reactions can also cause this paranoia.
If she's been diagnosed with dementia, I'd check with her doctor and tell him or her what is happening. There may be a medication change that can help.

Unfortunately, it's possible that this is a phase you must weather. If she trusts some non-family member, you could asked that person to repeatedly explain things to her. Many times, a non-family member is trusted more than a family member. Third party help can be invaluable.
Good luck. This hurts - I know. Many of us have been through similar situations.
Carol