The butcher should not be given any payment from the sacrifice as a fee
The Prophet Muhammad (peace be upon him) forbade giving any part of the sacrificial animal to the butcher as a fee. Imam Bukhari and Imam Muslim have narrated from Hazrat Ali (may Allah be pleased with him) that he stated:
أن النبى صلی اللہ علیہ وسلم أمره أن يقوم على بدنه، وأن يقسم بدنه كلها، لحومها وجلودها وجلالها، ولا يعطي فى جزارتها شيئا.
Indeed, the Prophet (peace be upon him) commanded them to oversee the slaughtering of his sacrificial camels and the distribution of their meat. And to distribute all their meat, skins, and the coarse cloths, and not to give the butcher anything from it as a fee for slaughtering, etc.
The wording of the hadith is from Sahih al-Bukhari.
Here the question arises whether it is permissible to give the butcher something from the sacrificial animal separately from the fee?
Imam Ibn Khuzaymah says about this:
إذا أعطى أجرته كاملة، ثم تصدق عليه، إذا كان فقيرا، كما يتصدق على الفقراء فلا بأس بذلك.
After giving the butcher the full fee, if due to his poverty, like other poor people, something is given to him from the sacrificial animal, there is no harm.
Imam Baghawi has also stated the same.
Warning:
However, it should be ensured that the butcher does not reduce or discount his fee on this basis. If there is such a concern, then safety lies in not giving him anything from the sacrifice.