"mina" indicates the subject is plural
"min" or "mitt" would be singular, eg "Jag älskar mitt barn" would be "I love my child".
barn is one of the nouns that is spelled exactly the same in plural
Min katt, mina katter = my cat, my cats
Mitt barn, mina barn = my child, my children
It's en katt in the singular, the singular definite is katten. The plural is katter and katterna. With the possessive pronoun, the distinction between definite/indefinite disappears (it's always definite as soon as you say min, since then you obviously know what you're talking about) and you get in the singular min katt and in the plural mina katter.
How on earth do you remember that...... So frustrating and the constant negative for something just slightly wrong is making pavlov one unhappy dog. Surely there is a way to tweek duo so rather than the constant negative slap on the wrist for a fine detail such as this there is a less negative and more constructive mechanism for learning the nuances.