What really a charge is apart from saying its a fundamental quantity. I mean IF in case of gravity, its curvature of spacetime due to mass so just like that can anyone explain how charge like properties come in place
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As far as I know, we don't really know what charge is besides an intrinsic property of objects. We mostly just talk about charged bodies. You can compare it to mass. We never exactly talk about what mass is. We just discuss properties related to it. – Satya Sep 15 '21 at 03:59
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1If you're asking whether we can interpret the EM forces in a geometrical was, as we can for gravity, then see Can all fundamental forces be fictitious forces?. – John Rennie Sep 15 '21 at 09:17
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ok, if what you are saying is true then, there is a lot more to discover about these properties. – Sankalp Yadav Sep 15 '21 at 10:13
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Related: https://physics.stackexchange.com/q/21753/109928 – Stéphane Rollandin Sep 15 '21 at 11:14
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in case of gravity, its curvature of spacetime due to mass
technically to the stress-energy tensor so energy density, energy flux, pressure, shear stress, momentum density, and momentum flux. But yes, for a stationary object with no internal stored / binding energy, it's just the mass. And we could also ask -- what is mass exactly? Elementary particles with same sizes have vastly different masses, so, like charge, it must be something "instrinsic" (... or at least its coupling to the Higgs field).
A charge (not electrical) is the generator of continuous symmetry. As per Noether's theorem, a continuous symmetry implies the existence of a conserved current (not necessarily electrical).
In the specific case of electrical charge, it is the generator of the U(1) symmetry associated with electromagnetism (QED). The conserved current is electrical current.
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"Color charge" is not the Noether charge corresponding to SU(3) (no such charge exists for there is no continuous global symmetry associated with the string force) - see e.g. https://physics.stackexchange.com/q/430935 (and same spiel for SU(2)) – Nihar Karve Sep 15 '21 at 05:20
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'the generator of continuous symmetry' This is a mathematical definition. I think the OP asks for a physical one. – my2cts Sep 22 '21 at 18:09