Has a Ḥadīth been narrated in which the Prophet (peace be upon him) said: "If my mother were alive, and the Ishā' prayer was established and began with Al-Fātiḥah, and the door of my house was open, and she called me, 'O my son, O Muḥammad,' I would leave the prayer and go answer her call," and what is its authenticity, if it exists?

There is no basis for this statement, and it is not permissible to attribute it to the Prophet, peace and blessings be upon him. A Muslim does not interrupt an obligatory prayer to answer the call of his parents; rather, he alerts them with a voice or recitation, then lightens his prayer and answers their call. As for a supererogatory prayer, he interrupts it to answer his parents.