how can a black hole emit radiation is nothing can escape its gravity?

You're thinking about a quasar.A quasi-stellar radio source, or quasar, is a very energetic and distant active galactic nucleus. Quasars are the most luminous objects in the universe. Quasars were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than extended sources similar to galaxies.

While there was initially some controversy over the nature of these objects—as recently as the early 1980s, there was no clear consensus as to their nature—there is now a scientific consensus that a quasar is a compact region in the center of a massive galaxy surrounding its central supermassive black hole. Its size is 10–10,000 times the Schwarzschild radius of the black hole. The quasar is powered by an accretion disc around the black hole.

Since quasars exhibit properties common to all active galaxies, the emissions from quasars can be readily compared to those of smaller active galaxies powered by smaller supermassive black holes. To create a luminosity of 1040 W, or Joules per second, (the typical brightness of a quasar), a super-massive black hole would have to consume the material equivalent of 10 stars per year. The brightest known quasars devour 1000 solar masses of material every year. The largest known is estimated to consume matter equivalent to 600 Earths per minute. Quasars 'turn on' and off depending on their surroundings, and since quasars cannot continue to feed at high rates for 10 billion years, after a quasar finishes accreting the surrounding gas and dust, it becomes an ordinary galaxy.

Quasars also provide some clues as to the end of the Big Bang's reionization. The oldest quasars (redshift ≥ 6) display a Gunn-Peterson trough and have absorption regions in front of them indicating that the intergalactic medium at that time was neutral gas. More recent quasars show no absorption region but rather their spectra contain a spiky area known as the Lyman-alpha forest. This indicates that the intergalactic medium has undergone reionization into plasma, and that neutral gas exists only in small clouds.

One other interesting characteristic of quasars is that they show evidence of elements heavier than helium, indicating that galaxies underwent a massive phase of star formation, creating population III stars between the time of the Big Bang and the first observed quasars. Light from these stars may have been observed in 2005 using NASA's Spitzer Space Telescope, although this observation remains to be confirmed.

Great question! A lot of people have asked this same question, so you may want at look at there answers too.

That radiation is actually x-rays and material being accelerated into the black hole itself or into a torus around it. The material is accelerated to almost light speed by the black hole's immense gravity and friction within that high-velocity material generates radiation. All of it will eventually be drawn all the way into the black hole, but at that moment its expelled but will get sucked back in and that's what we can detect on Earth.

Some may say its hawking radiation but that isn't entirely true because it has never been observed or proven and is just a theory fyi

Nothing within the event horizon or inside it can escape it. However, some things right on the outside CAN escape. That's the principle of Hawking's radiation. If you have pair production right outside it (for example a few milimeters or micrometers on the outside), one particle of the pair can fall in while the other manages to escape.

That quantum prediction, "Hawking Radiation" is not from the B.H. itself
but from 'virtual pair creation' at it's event horizon.
The particle outside can theoretically escape.