The correct way to express the concept of being in charge is:
* In charge: This is the most common and preferred way to express the concept.
* Responsibility: This emphasizes the duty or obligation.
* Leadership: This emphasizes the role of guiding and directing others.
* Management: This implies overseeing and coordinating a group or activity.
If you are trying to express the state of being in charge, consider using one of these alternatives instead of "inchargeship."