In the baptism record, the child is recorded as the base son of Spinster. I have the name of the child and mother. How do I record the fact of "Base Son" with no name of the father
Are you indexing, or are you attaching the record to someone?
If you are indexing, that information doesn't need to be recorded. Just mark the Father's information as blank.
If you are talking about a record you are connecting (or is already connected) to the tree, do not add a father to the tree, but do add a note to the child and mother that explains the situation.
I'd just attach the child to the mother leaving the father blank and then attach the source to both child and mother