If two cells are connected in parallel, say,

                  1      2
         ________||_____||_______
                 |      |
             
              1->10V  2->5V

Just consider the double line as the positive electrode and the single line as the negative (sorry, I don't know how to put in pictures).

I understand that charge from cell 1 have a potential of 10 V would increase it's potential by 5V on moving through the second cell (neglecting internal resistance).

But since both are cells, doesn't the 5V cell have the capability to produce charge as well? The charge coming from that cell should only have a potential of 5V

I know this theory is definitely wrong but I want to know why. I think it's because of the way the cells are connected but I'm sure. In any case, even if I'm right, please elaborate.