The core of a star is located inside the star in a region where the temperature and pressures are sufficient to ignite nuclear fusion, converting atoms of hydrogen into helium, and releasing a tremendous amount of heat.
The size of the core depends on the mass of the star. For example, our Sun measures 1,391,000 km across and is a fairly normal star. The core of the Sun makes up about 20% of the solar radius; about 278,000 km across. It’s within this region that temperatures reach 15,000,000 Kelvin and nuclear fusion can take place. Fusion doesn’t take place in any other part of the Sun.
As you know, stars can be larger or smaller than the Sun. Larger stars will have larger, hotter cores. The largest stars have cores of 18 million Kelvin, and inside this region hydrogen is fused into helium using a different process called the CNO cycle.
The least massive star capable of sustaining fusion in its core is about 7.5% the mass of the Sun. Below this size, temperatures are too low and you end up with a brown dwarf.