I get codes p0700 & p0562. I changed the alternator, the battery light still on

Hello, the P0700 is transmission related, but may be erroneous and related to low system voltage. The P0562 is related to low system voltage. You're going to need to look further to ensure the replacement alternator is functioning as it should be. Also have a close look at the wiring connector at the alternator to ensure it is clear of any damage or melting.