There are some types of wood that are better suited for this type of situation than others, but that can greatly affect the species of fish you keep in the tank. Welaby wood is a very hard wood, very dense and heavy, but it also contains more tannic acid than most other woods, which will soften the water at an uncontrollable rate. Welaby wood tends to have fungus/mold problems less than most others, but there still is no guarantee. Any wood can develop fungus and mold issues.
Treatment for the mold when it comes to wood is very limited. Avoid bleach, as this tends to cause the wood to rot and can take months to dry completely through to be fish safe again. If there are no animals or fish in the tank an antifungal medication treatment in the water can sometimes be effective.. but I would not suggest this if there are already animals in the tank. Keeping tank water extremely clean can help, but generally when this sort of thing happens the fungus is usually feeding off of something within the content of the wood or the wood itself.
The only other option I can think of off the top of my head is to coat the wood in an aquarium safe clear resin to completely seal it. This will bring other challenges, again depending on the type of wood... it may rot once completely sealed, some at a faster rate than others and would be a bit messy and could get expensive depending on the size of the wood piece.
The ultimate solution is to find a fake piece that looks like real wood or try to find petrified wood to use to create your decor. Try shopping reptile supplies, that is the easiest place to find artificial pieces that look like the real thing. Plastic, polyresin, and acrylic pieces are fish safe provided they have either been bleached after use with reptiles or are rinsed thoroughly before put into the tank if they are new.