Do the children sin if they cut ties with their paternal aunt who caused their father to be imprisoned, did not acknowledge her mistake, and did not inquire about them? And what is the ruling on the father's statement to one of his children: "I will not forgive you if you speak to her"?

If your paternal aunt has unjustly and aggressively harmed your father, she is an offender and has severed her ties of kinship. She should be advised to repent and seek your father's forgiveness. Nevertheless, a paternal aunt remains a relative with whom ties of kinship must be maintained and not severed. However, she may be boycotted due to her disobedience if there is hope that the boycott will be beneficial; otherwise, it is better to abandon it. If harm is feared from visiting her, then ties can be maintained in a way that causes no harm, such as through phone calls. If the father forbids his son from maintaining ties with his paternal aunt, then he should not be obeyed, as he is commanding an act of disobedience. The son should explain this to his father kindly, and if the father insists, then his brother should maintain ties with their paternal aunt wisely, without their father's knowledge.