My tax return was rejected by both the state and fed, and I believe it was because of my 1095-A. How do I attach this to my returns?

You don't attach the form 1095-A. You enter the information from the 1095-A in TurboTax. In the Search box type 1095-a, then click the link that says "Jump to 1095-a."

the 1095-A info is transferred to form 8962 which must be completed. it's the 8962 that the iRS is looking for.