Well, I've had no luck finding a likely match. Unfortunately, the bit you memorised is an extremely common combination of syllables in Polish. I've been searching for similar phrases. Maybe someone else can help. Not even you can be sure that you heard correctly, and the possibilities are endless.
"to my a jak" would literally mean, "that's us, but when..."
"to mija jak" would mean, "it passes as though"
"to ma, a jak" would mean, "... has got it, but when"
"to miała jak" would mean, "... she had got it like"
"to moja k-something" would mean, "this is my k-something"
"ta moja k-something" would mean, "that k-something of mine"
"domy jak" would mean, "houses like"
"tu, my jak" would mean, "here were are as"
"oddał mu jak" can possibly mean "he gave it back to him like".
To complicate things further, any Polish verb can end in "-my" in the first person plural. "Ja" also means "I" and any number of words can begin with "k-", not to mention the innumerable words that have "ja" as their first or final syllable.
