Do customer orders have higher priority than market makers' orders in the US OTC stock market?

In the US OTC stock market, do customer orders have higher priority than market makers’ orders? For example, a market maker is bidding on stock S at $10 for 100 shares. Assume that this is the highest bid, and that the quotes do not change. A few moments later, I similarly place a bid on stock S at $10 for 100 shares. Does my order have priority over the market maker’s order?

From my understanding, customer orders at the NYSE have priority over the specialists’ orders. I am wondering if this is the same for other markets such as the US OTC stock market.

(By "OTC stock market", I mean the market for stocks that are not listed on a stock exchange. For example, the OTC Pink market (pink sheets)).