Yes， it is possible for parents to continue to dispute custody of their child even after the child has turned two years old.
In many countries， the best interests of the child are the most important consideration in custody cases， and this can include factors such as the child's age， developmental needs， and current attachment to each parent. Therefore， just because a child has turned two years old does not automatically mean that custody arrangements will remain stable or that disputes will no longer arise.
Additionally， parents may experience changes in their circumstances that lead them to seek a modification of custody or visitation arrangements， such as a relocation for work or a remarriage. In some cases， one parent may also allege that the other parent is no longer acting in the best interests of the child and may seek to modify custody or visitation based on evidence of neglect or abuse.
Overall， while custody disputes may become less common as a child gets older， they can certainly continue beyond the age of two. It is important for parents to prioritize their child's needs and well-being and to work towards cooperative and respectful co-parenting， even in the face of disagreements or disputes.
