IRS requesting form 8962 and 1095-A but I do not have Health Insurance Marketplace... I used a private health insurance from my school (blue cross). What should I do?

The IRS is asking you for form 1095-A and form 8962 because they have found a form 1095-A which matches your SSN.

If you are sure that you did not have any Marketplace policy, then it may be an error from the IRS (It sometimes happen!). You can then write back to the iRS stating that in 2019, you were not covered by a Marketplace policy and do not have any form 1095-A.