I am not sure of what you mean by “psychic power”.
I’ve been meditating for over 45 years. Before children (more than 30 years ago), I’d meditate as much as 3–4 hours in a sitting. I had numerous “mystical, non-corporial” experiences, some out-of-body ones, and prophetic dreams.
I did NOT have the wisdom to effectively handle the experiences.
My experience over the years (my own as well as observing others) has led me to believe that youth (emotional & mental) tends toward ego.
Thus “psychic power” is expressed from the position of ego. Dangerous - potentially harmful - stuff.
It is challenging to balance the needs/wants of ego with the wisdom of spiritual awareness; it can be done more easily if one approaches meditation as a process of connecting with Spirit & strengthening that connection via consistent meditative practice.
Meditating to gain psychic power will end up biting you in the ass.
However, if meditation is about connecting & strengthening that connection - and during that practice one has “psychic” experiences, then it may be wise to just observe. Or you might want to keep a notebook - recording the experiences. You will learn in time what to do - if anything - with these experiences.