I have been trying to achieve this effort for a while using the circular gradient and then another layer of linear-gradient however, I am not able to figure it out. Any help will be appreciated or just pointers.
One easy way to make an approximate replica is to draw three overlapping blurred ellipses on a black background. The opacities are different. I experimented in Inkscape because sizes, colours, the amount of blur and opacities were easily adjustable. In Photoshop everything is much more complex to adjust. If you have Illustrator, use it.
Top left version is your example. Top right version is mine. Top middle version is the same but without clipping mask. In the bottom there are the ellipses moved apart on black.
There is a lot going on with this image. It looks like multiple gradients linear & elliptical as well as some layering / masking with some blending modes. I see ~3 elliptical gradients. There seems to be one on top, bottom and one overlapping in the middle which gives the larger spot on bottom the appearance of blending into the spot on top. I think the elliptical gradients may also be on top of a linear gradient as well as a linear gradient applied on top to help blend in each gradient layer. Finally some layer masking was incorporated to paint back in some desired light and darks around the edges of the gradient layers. There’s no quick formula to how this one was done, it was definitely fine tuned.