I went to school in Fall of 2019. However I paid my bill in 2020. Would I claim this tuition in 2019 or 2020 taxes?

If you paid your tuition in 2020, you can only claim it as education expenses on your 2020 tax return (next year).

I'm afraid the answer is neither.  To qualify for a tuition credit or deduction,  you must pay in the year the courses were taken  or for the  first term of the following year.  Paying for the Spring 2020 term, in 2019, would allow you to claim the credit in 2019.  But paying for 2019 courses, in 2020, does not allow you to claim anything in either year.