Based on this “Little Red Riding Rabbit” TVTropes page, ta have is an affectation of Red:

Verbal Tic: Red ends a lot of her lines with the exclamation “Ta’ Have!”, just another thing that makes her so very irritating.

The Likely Looney, Mostly Merrie blog reports:

Red is stereotyped as a loud, obnoxious bobby-soxer teenager - vocalised irritatingly by Bea Benaderet with great comedy values. . . . The character was the inspiration of radio comedian Cass Daley - and Michael Maltese’s young daughter! Daley was known for her energy and loudness; but some of Red’s childlike dialogue (“ta-have!”) was adapted from Maltese’s daughter.

This is backed up by the TVTropes Trivia page for “Little Red Riding Rabbit”:

According to Mike Maltese’s daughter, Brenda, “I was that obnoxious girl [in the Bugs Bunny cartoon’ Little Red Riding Rabbit.’]” Brenda used to shout “Ta have!” as a girl and Mike put it in the story. When this cartoon was released in 1944, Brenda Maltese was not quite six years old, a little young for the part, so she was drawn as a teenage bobby-soxer, in a parody of comedienne Cass Daley.

You can see the full version of “Little Red Riding Rabbit” and all of Red’s ta haves at https://archive.org/details/looney-tunes-s-1944e-01-little-red-riding-rabbit.

So, unless you can find instances of ta have uttered by people other than Red or those inspired by her, to have means nothing beyond the usual sense of to own or to possess.

Based on this “Little Red Riding Rabbit” TVTropes page, ta have is an affectation of Red:

Verbal Tic: Red ends a lot of her lines with the exclamation “Ta’ Have!”, just another thing that makes her so very irritating.

The Likely Looney, Mostly Merrie blog reports:

Red is stereotyped as a loud, obnoxious bobby-soxer teenager - vocalised irritatingly by Bea Benaderet with great comedy values. . . . The character was the inspiration of radio comedian Cass Daley - and Michael Maltese’s young daughter! Daley was known for her energy and loudness; but some of Red’s childlike dialogue (“ta-have!”) was adapted from Maltese’s daughter.

This is backed up by the TVTropes Trivia page for “Little Red Riding Rabbit”:

According to Mike Maltese’s daughter, Brenda, “I was that obnoxious girl [in the Bugs Bunny cartoon’ Little Red Riding Rabbit.’]” Brenda used to shout “Ta have!” as a girl and Mike put it in the story. When this cartoon was released in 1944, Brenda Maltese was not quite six years old, a little young for the part, so she was drawn as a teenage bobby-soxer, in a parody of comedienne Cass Daley.

You can see the full version of “Little Red Riding Rabbit” and all of Red’s ta haves at https://archive.org/details/looney-tunes-s-1944e-01-little-red-riding-rabbit.

So, unless you can find instances of ta have uttered by people other than Red (minus those inspired by her), to have means nothing beyond the usual sense of to own or to possess.