I entered 1098-T info-Box 5/Scholarship amount was greater than Box 1/Tuition. Net amount was different due to an amt add tax-free assist line 15 on Stdt Info Sheet. How?

"New question on 2021 Form 1098-T - if part of tuition in Box 1 is for 1st semester in 2022, can I still include the amount for 2022 as qualified expense on my 2021 return?"

Yes, payments for expenses of 2021 and/or the first 3 months of 2022.

You can the expenses in the tax year it was paid.

According to the IRS:

"Prepaid expenses. Qualified education expenses paid in 2021 for an academic period that begins in the first 3 months of 2022 can be used in figuring an education credit for 2021 only. See Academic period, earlier. For example, if you pay $2,000 in December 2021 for qualified tuition for the 2022 winter quarter that begins in January 2022, you can use that $2,000 in figuring an education credit for 2021 only (if you meet all the other requirements)."

"Also, if part of scholarship in Box 5 is for 1st semester in 2022, can I deduct that amount but then add any amount from my 2020 tax return that was for 2021?"

I might be unclear as to your question here. What amounts do you want to add?

You report the scholarship in the same tax year that the expense is posted.

If a scholarship posts in 2021, and it covers expenses for 2022, subtract it out if Box 1 does not also report the payment. 

If a scholarship posts in 2021, and it covers expenses for 2022, do NOT subtract it out if Box 1 includes that same payment. 

You can't add expenses PAID in 2020 on your 2021 return. 

So if classes that started in 2021 were paid in 2020, you can only claim that expense on your 2020 return. 

You can allocate scholarships (Box 5) to the year of when those classes started, but you can't move payments. Payments (Box 1) can only be claimed the year they are paid. 

Yes, tax years and calendar years overlap, so you need to keep payments and scholarships straight. Use your student account as well.