Are there autotrophic fungi?
no none of the fungi in the nature is  autotrophic.
they are dependent mostly upon dead and decayed matter.
the reason that they are not autotrophic is that they lack any type of photopigment to carry out photosynthesis.
photopigments are necessary because the are the only components that can trap the solar energy and use it to extract the electrons from the inorganic source such as h2s or h2o by splitting them which are further used to prepare ATP and NADPHH+. these 2 are the assimilatory powers for the further dark reaction. so if these are not there then the processes of photosynthesis would not be there and therefore the organism will not be able to produce its own food in turn it would depend on other autotorphs for food (in case of fungi dead and decade matter).