How does strong fundamental force hold a nucleus?

An atomic nucleus contains positively charged protons and neutral neutrons. If there is more than one proton, electrostatic repulsion tries to push them apart. Neutrons are required to make a nucleus with more than one proton stable.

The strong nuclear force is responsible for binding protons and neutrons together to form a nucleus.

The strong nuclear force is stronger than the electromagnetic force. The first stage of fusion reactions in the Sun is that when two protons get close enough together the strong nuclear force will overcome the electrostatic repulsion and bind them into a biproton also known as Helium-2. The electrostatic repulsion makes this nucleus very unstable. Most of the biprotons disintegrate back into two protons. Occasionally the weak nuclear force will convert a proton into a neutron to make stable Dueterium also known as Hydrogen-2.

Actually the strong nuclear force doesn't exist. Protons are made up of two up quarks and a down quark. Neutrons are made up of one up quark and two down quarks. The colour force binds the quarks together into protons and neutrons. The strong nuclear force is actually a residual effect of the colour force which binds the quarks in a proton or a neutron with the quarks in other protons and neutrons.

The strong nuclear force, one of the four fundamental forces of nature, holds the nucleus together by overcoming the electrostatic repulsion between positively charged protons. It acts over very short distances, binding protons and neutrons together in the nucleus through the exchange of particles called gluons.