The menu you are referring to is controlled by the UIMenuController.
Customise the menu items like:
UIMenuItem *menuItem = [[UIMenuItem alloc] initWithTitle:@"Do Something"
action:@selector(aSelector:)];
[[UIMenuController sharedMenuController] setMenuItems: @[menuItem]];
You will have to implement canPerformAction:withSender:
in a custom view class.
NSHipster has a nice article.