I work for a City and every month we get a mid-month draw. I've heard that this is not a good practice or maybe illegal.
More like it is complicated. Governmental employers are not subject to the same rules as non-governmental employers. You did not mention your state. Payment requirements are a function of state law. You need to contact your state's DOL and find out what the payment requirements are for a governmental employer. See if monthly payments are legal. If not, see if the draws somehow comply with whatever the state rules are.
Regarding draws, those are normally associated with inside sales commissioned employees. They are paid a "draw", generally minimum wage, then monthly/quarterly/whenever (see state law) commissions due are calculated. If this number exceeds the draws paid, then an additional payment is made.
When payments are due are always very much a state law question, and the answer is almost always different for governmental employers. Draws are both a federal and state law concept, generally associated with commissioned inside sales (but not necessarily required to be). CA is the only state that I am reasonably familiar with, but I have not ever had to worry about governmental employers. If I was researching a governmental employer in CA, I would start with the Wage Orders (industry specific regulations) or maybe the CA-DLSE enforcement manual.
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