Is it permissible to slaughter a calf instead of three sheep vowed for the birth of a child, with the intention of two sheep for the aqiqah and one for the vow, due to preferring calf meat and the difficulty of paying the price of the sheep all at once?

Scholars have differed regarding the necessity of fulfilling a vow exactly as it was vowed. The more cautious approach is for the one who made the vow to fulfill it as specified. However, if they substitute it with something better, it is sufficient. Thus, a cow suffices for seven sheep. It is permissible to slaughter a single cow for both a vow and an 'Aqiqah simultaneously, such that each seventh of it corresponds to one sheep. In this case, three-sevenths of the cow would be for the three sheep vowed, and two-sevenths for the 'Aqiqah. As for the questioner's statement, "I wish to purify my newborn," if he means circumcision, there is no established Sunnah for a circumcision feast. Rather, the Sunnah concerning a newborn is to perform the 'Aqiqah for him. It is permissible for seven people to share in a camel or a cow for sacrifice, whether they are from the same household or separate, or if some of them desire the meat, and whether it is a vowed sacrifice or a voluntary one.