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I want to inset and then scale the mesh on a curved surface. How do I do that? Since i cannot inset beyond a certain point. I want the scale to conform with the shape of the original shape. It should just slide like skin along the surface. How can I do it? enter image description here

enter image description here

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From your current topology it seems complicated, also you should tell what is your final goal, but you could redo something similar this way:

Create a cube, create a UV sphere, give your cube a Boolean modifier (Intersect mode) with the sphere as boolean Object:

enter image description here

Apply the modifier, select all in Edit mode and press M > Merge by Distance, in the Operator box set the Merge Distance to 0.05. There are still some isolated vertices, remove them with a CtrlX:

enter image description here

Deselect the flat faces and inset:

enter image description here

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