Can we compress any object to create black Holes? In general, when a star runs out of nuclear fuel, gravity gets the upper hand and the material in the core is compressed even further and creates black holes. I am clear till  here.
Now the question is: Does that depend on the mass of the star (or object)?
Naturally, the more massive the core of the star, the greater the force of gravity that compresses the material and easy to create Black Hole.
For smaller stars, when the nuclear fuel is exhausted and there are no more nuclear reactions to fight gravity, the repulsive forces among electrons within the star eventually create enough pressure to halt further gravitational collapse. The star then cools and dies peacefully.
In science videos and discussions is said that we can create black holes from any object. For example, if we are able to compress Earth to the size of the tennis ball, can we then create a black hole?
Isn't the nuclear fusion / reaction necessary to create a black hole? Of course, to fight against gravity we may require some kind of energy in this case, Nuclear reactions. But I am generally concerned like, does Nuclear Reaction is only to fight gravity, it does not play any other role in creating Black Hole.
Do you mean, "Can we in principle", or just, "Can we..." ?

The answer to the latter is no. We have no technology to create black holes. It was a remote possibility that was considered when creating the high energy densities in the LHC, but in practice the energies aren't high enough.

Can we in principle do it? The answer is yes. If you can squash enough mass (or energy) into a very small volume then the inevitable consequence is a black hole.

Most would say that the volume in question is governed by the Schwarzschild radius, $r_s$  which is roughly 3km multiplied by the mass in solar units. Thus for an Earth mass $r_s$ is about 1 cm.

Actually the radius within which collapse to a black hole is inevitable is a little bit larger because even the "hardest" equation of state, where the speed of sound equals the speed of light, cannot resist collapse at radii below about $1.5 r_s$.

The problem is that to compress materials this much would be incredibly difficult. For the example of an Earth mass, we are talking densities of order $10^{30}$ kg/m$^3$. But (long) before you got to that stage, yes you would have the problem of overcoming the nuclear fusion reactions would be initiated that would oppose your compression (ie you would end up making a mini-star before you could get to a black hole). Because the Schwarzschild radius depends linearly on mass, then less massive black holes need to be even denser. However, we are again talking about "in principle". So assuming compression could overcome the various opposing forces, then a black hole could be formed.

It really doesn't matter what the black hole is made of. In a star, the sequence of nuclear fusion events is a consequence of the physical conditions in the stellar interior. It is not anything that is required for black hole formation.