Charles Ellicott Commentary Leviticus 4:35

"and all the fat thereof shall he take away, as the fat of the lamb is taken away from the sacrifice of peace-offerings; and the priest shall burn them on the altar, upon the offerings of Jehovah made by fire; and the priest shall make atonement for him as touching his sin that he hath sinned, and he shall be forgiven." — Leviticus 4:35 (ASV)

According to the offerings made by fire. —Better, upon the offerings made by fire. As the daily morning sacrifice was offered first every day, and as it continued burning on the altar all morning, no fresh or special fire was to be kindled for it, but it was to be upon the fire sacrifices which had already been placed there before. (Leviticus 5:12.)

The flesh of the sin offering, both for the prince and for the individual members of the community, was not burnt outside the camp, as was the case with the flesh of the sacrifice for the high priest and for the whole congregation, but was the perquisite of the priests, and was eaten by them (Leviticus 6:26–30). This is in harmony with the law. The sinner who brought the sin offering could not partake of it. Hence, the priest was not permitted to eat of the flesh of the sin offering which he offered for himself, or of the flesh of the congregational sin offering, because he was a member of the congregation.