The Passuk in Vayikra 11:42 says that anything that slithers like a snake “Lo sachileim” (do not feed them) as they are disgusting.
The Gemara in Yevamos 114b learns out from three places that one may not feed a child a forbidden food. The above passuk is one of the three places.
The question arises can one feed a child on Yom Kippur? Since the child may eat for his health, there would be no problem in feeding him. Or is it forbidden for the adult to feed him, and the child will need to get his own food.
The Magen Avraham 619:9 says it is assur. The Mishna Berurah 25 agrees with him. In the Shaar Hatziyun the Mishna Berura differentiates between a child the age of eleven and or twelve there it would be forbidden whereas a child younger than that it would be permitted. The reason is that a child eleven or twelve must complete the fast Mi’de’Rabbonon. Whereas a younger child just has to fast for a few hours.
The Minchas Chinuch 313:10 says it is forbidden to feed a child from the minute the child is born anything more than necessary for the health of the child. Since it is hard to determine what is needed, one can feed a child up to the age of eight as much as he wants. After eight we don’t make the child fast, but we don’t feed the child either. The Shailos Utshuvos Zichron Yosef 7 argues on the Minchas Chinuch and says that feeding a child on Yom Kippur is different as the food is not an object of issur it is kosher food therefore one can differentiate between forbidden food and food which is permitted but the time does not allow it to be eaten i.e. Yom Kippur. He explains that since Yom Kippur the inyan of not eating is an “inuy”(pain), and a child does not have the chiyuv of inuy. Therefore an adult would be permitted to feed the child.
The Shailos Utshuvos of Teshuvos BeHanhagos 188 says that in Shuls where there are children who are not fasting on Yom Kippur and are given nosh and candy that would not be allowed. It is only food that is necessary for the child to eat that would be allowed to be given. It is not assur for the child to take for himself as he is not mechuyav in inuy he just has to fast minimal hours. The bottom line is that one can feed a child healthy food as he needs to be healthy and can’t fast but there would be very little justification to feed him sweet foods.