If none of the available profiles is close enough to your species, then you might consider training Augustus yourself. While this might be a little difficult, I find that using BUSCO v4 (I think newer versions don't use augustus anymore) can make it much easier. BUSCO will automatically train Augustus and make a new profile which you can then use to predict genes. Another thing you should note is that ab-initio gene prediction (which is what Augustus does) is a noisy and often inaccurate process. It is usually only one step in a large genome annotation pipeline. To get a good annotation, you'd probably want to use evidence such as transcripts, RNA-seq, and protein sequences, in the context of an annotation pipeline like MAKER, PASSA, or EvidenceModeler.

There are many fungal species that are known to augustus:

https://bioinf.uni-greifswald.de/augustus/

Usually you select the one known or suspected to be closest to your species of interest. It is not a bad idea to try more than one.