I get up between 4 and 5 in the morning to learn before davvening. Davening is at 6:30 and on Shabbat it is at 8:30,but I still get up between 4 and 5. When I get dressed should I say the beracha “al mitzvah Tzitzit” on my tallit katan since I won’t be saying the beracha for the big tallit until much later? Or should I still wait to say the beracha for the big tallit and let that cover the tallit katan even though it may be 2-3 hours from when I put on the tallit katan until I put on the tallit gadol? Please send sources. Thank you.
You should not recite the berachah, but should rely on the berachah you make on the Tallis later.
See Mishnah Berurah 8:24 which mentions that the custom is that even if there is a long wait between the tallis katan and gadol, no berachah is made (he notes the reason as being that on occasion the tallis katan is not worthy of a berachah, and that therefore it is customary to make the berachah specifically on the tallis gadol).
In the case of the question, the tallis can be worn a little earlier, and the berachah made before the beginning of davening.