there is no evidence that he did or didn't wear them. I believe that he didn't.
http://secondexodus.mobi/tzitzit/
Rabbi Yeshua Wore the Tzitzit
We know that
Rabbi Yeshua wore the tzitzit (tassels or fringes). The tzitzit were to be worn at all times, “to look upon and remember all the commandments of the Lord, to do them”
Num 15:39. Rabbi Yeshua probably wore his tzitzit as part of a talit katan, the small talit worn every day under the outer clothing and often called simply the tzitzit. The tassels may hang below the shirt so they are visible to passersby. Rabbi Yeshua certainly wore the talit gadol, great prayer shawl, at Temple prayer.
The tzitzit are God’s sign among the people Israel. The Septuagint used the Greek word kraspeda for tzitzit. God commanded Moses, “Speak to the people of Israel, and bid them to make tassels [kraspeda] on the corners of their garments throughout their generations, and to put upon the tassel [kraspeda] of each corner a cord of blue”
Num 15:38. St. Matthew used the same Greek word when describing the Pharisees. “They make their phylacteries broad and their fringes [kraspeda] long”
Mt 23:5.
St. Matthew tells us, “And behold, a woman who had suffered from a hemorrhage for twelve years came up behind him and touched the fringe [kraspedou] of his garment; for she said to herself, ‘If I only touch his garment, I shall be made well’”
Mt 9:20-
21. St. Luke used the same word. “And a woman who had had a flow of blood for twelve years and had spent all her living upon physicians and could not be healed by any one, came up behind him, and touched the fringe [kraspedou] of his garment; and immediately her flow of blood ceased”
Lk 8:43-
44.
So we know that the woman touched Rabbi Yeshua’s tzitzit. She knew that, “wherever he came, in villages, cities, or country, they laid the sick in the market places, and besought him that they might touch even the fringe [kraspedou] of his garment; and as many as touched it were made well”
Mk 6:56.