Please let me know if there are experiments or data that show it
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Yes there is evidence that they do. For example Rutherford's experiment shows that protons repel each other (via Coulomb interaction). This is because they are positively charged particles.
There are of course, other forces involved like the strong force which is what binds nuclei together, but its range is much shorter so it is very difficult to bring them together (that is why very high temperatures and pressures are needed for nuclear fusion).
Also note that the repulsion between protons led scientists in the early 20th century to believe that it was impossible to harness energy through nuclear fission. The neutron was not known so the only possible way to catalyse fission would be to fire protons to nuclei but the Coulomb force made them think this was impossible on a large scale (the chain reaction would not be sustainable).