The Halacha requires that in order for a garment to be obligated in Sisit, at least the majority of its sides must be open. If the majority is closed, even though the garment has four corners, it is not obligated in Sisit. The Shulchan Aruch (Siman 10) rules that if the sides were open and then were fastened together with stitches or with another means that requires a significant action to re-open, the garment is considered closed and is exempt from Sisit.
The Poskim discuss the status of a garment closed with buttons or snaps. They establish a general principle by which a "tight" fastening mechanism is considered closed, and an easily opened closure, is still considered open. However, it is not clear exactly how to apply this. There is no authoritative ruling whether snaps and buttons are considered like stiches or not. Therefore, the English Yalkut Yosef recommends not putting buttons or snaps, especially on a Tallit Katan, in order to avoid doubt whether one fulfilled the Misva. However, one snap or button, immediately below the armpit is permitted, because it leaves the majority of the sides open.
SUMMARY
It is best not to use a Tallit Katan that is fastened on the sides with buttons or snaps.
