Is it permissible for me to file a lawsuit to increase the previously decreed child support of 600 riyals, given that it is insufficient and the father of the children is financially capable?

Children's maintenance is estimated based on sufficiency. If the mentioned amount is not enough for the children's maintenance, there is no harm in raising the matter to the Sharia judge and demanding an increase. A well-off father should not be content with just the sufficient amount, but rather should be generous with them, for Allah Almighty says: "Let a man of wealth spend from his wealth, and he whose provision is restricted - let him spend from what Allah has given him. Allah does not burden a soul beyond that which He has given it. Allah will bring about, after hardship, ease." (At-Talaq: 7), and for what was reported from the Prophet, peace and blessings be upon him: "The greatest reward is that which you spend on your family."