My mom and I share policy and are filing taxes separately. don't understand how to fill out 1095a/8962?

You will each enter that you share the policy with another person (unless she claims you then she will enter it on her return only).  Then you will be asked for her SSN and name and how much you want to allocate to you and how much to her of the premiums and credits.  You can allocate from 0-100% for each of you, but your total must equal 100%. 

would it affect the next year’s premium?

Each tax year is filed independent of other years, so no, how you allocate your premiums and the tax credit this year will not affect next year.