The Messenger of Allah ﷺ said, "Each of you is a shepherd, and each of you is responsible for his flock. The ruler placed over the people is a shepherd over them and is responsible for them. A man is a shepherd over his household and is responsible for them. A woman is a shepherdess over her husband's house and his children and is responsible for them. A man's servant is a shepherd over his master's property and is responsible for it. So indeed, each of you is a shepherd, and each of you is responsible for his flock."
حدثنا يحيى عن عبيد الله أخبرني نافع
قال رسول الله ﷺ كلكم راع وكلكم مسئول عن رعيته فالأمير الذي على الناس راع عليهم وهو مسئول عنهم والرجل راع على أهل بيته وهو مسئول عنهم والمرأة راعية على بيت بعلها وولده وهي مسئولة عنهم وعبد الرجل راع على بيت سيده وهو مسئول عنه ألا فكلكم راع وكلكم مسئول عن رعيته
Its chain of transmission is sahih. It is a repeat of 4495, and see also 4637. Regarding his saying "and his child," in one manuscript version, in the margin of M, it reads "and her child."