Barna is the definite plural form of the word
barn, and it means "the children". Because it is plural, you'd have to use
mine rather than
mitt, producing the sentence
Barna er mine.
Edit: Also, "barna" ≠ "barnet". This may be confusing because "-a" is used as an ending for both definite singular feminine (e.g., "jenta") and definite plural neuter nouns (e.g., "barna"). :P