I have tried vermi-composting in an apartment, and despite the theoretical lack of fruit flies, I was never able to eliminate this problem in reality. Since you have a balcony, fruit flies may not be an issue for you. Instead, you will need to deal with the minimal level of maintenance for the worms, which need to be checked on occasionally, given bedding such as newspaper, and you will need to give them a home with ventilation and drainage.
Another option is to buy one of the engineered devices that performs composting for you at home, maintains proper temperature, etc. This option can be pricey.
But I am wondering why you are interested specifically in composting at home, i.e. transforming organic waste into rich humus (for soil)? It sounds like you are more interested in having your organic waste composted, rather than making the humus yourself. In this case, you may be interested in separating your organic waste for someone else to compost, rather than composting it yourself.
I have started simply storing my compostable waste and then delivering it to a composting collection rather than trying to compost at home. This is much simpler, assuming that there is a convenient drop-off point for you. The difference here is that to store the waste, you just need a leak-proof container with a filter and good seal. These are sold all around the city as compostable waste containers. When your home bin gets full, dump the contents into the larger collection bin. Perhaps you could arrange with others in your apartment building so that you can have one larger shared bin in the basement with a weekly collection service? Else, you can deliver your own material to some community compost bin.