Need to update related records based in a field value from the parent record. If I use with sharing in class, just the records that the current user has access will be updated?
That's correct. You won't be able to query records the user does not have access to, nor will you be able to update records the user has read-only access to. The four main permissions, Create, Read, Update, and Delete (CRUD) are honored when using
with sharing, but Field Level Security (FLS) is not honored, so you need to make sure to use Security.stripInaccessible if you want to prevent updating fields the user does not have edit permission on.