Yes you will, its not a click bait neither I am joking with you it's science and only science. It's all about how gravity affects time. And yes you age a little bit less in mountains but it is rather negligible.
How gravity affects time?
For this you must know what space time is and how gravity is;
Then what is space time and how gravity works?
Space time is a term given by Einstein because he thought space and time are very much interlinked to each other and should be termed in a same term. Space time is like a fabric to support everything in this universe. You may think space is empty and has no works but you are wrong. Space, rather sat space time supports earth, sun and everything. Gravity works because masses curves those space time fabric and masses gets attracted to each other.
Take this as an example
How gravity affects time ?
Here comes the little click bait kind of thing. We won't be younger in mountains rather it is just the opposite. It goes this way, you will be little bit older than your friend living in plain if you live in mountain for some time. It is because the speed of light is always constant and gravity affects light. To make the speed of light constant time must slow down in gravity. So, in black hole time stops.
Gravity affecting time is also a key theory for time travel !
