LAN9512 differential wire routing on PCB
The smaller in width you want your microstrip lines, the thinner your dielectric between ground and signal must be to obtain the required impedance. There's not a lot of getting around that, aside from changing the dielectric constant of your material (but that's usually expensive).

You say you're using a 4-layer PCB, what you may want to consider shopping around for different material stack-ups, or inquiring about custom stack-ups. The stack-up is the layer-by-layer description of the cross section of your PCB. Some places will divide the insulator layers equally (e.g. 0.4mm dielectric between all layers for a PCB), and some will have a thicker middle insulator (between layers 2-3) and thinner outer insulators (between layers 1-2 and 3-4). OSH Park does an assymmetric stack-up, you can see their documentation here.

Asking people to do non-standard (to them) things will likely incur extra costs, and if you need to get down to 0.1mm, that may be on the "more exotic" side of things.