The answer to the question, do Robinhood penny stocks under $1 exist, is unfortunately going to disappoint you. The simple answer is no.
Robinhood restricts penny stock trading due to the volatility nature of investing in penny stocks. Not only does Robinhood not allow short selling, so you cannot short a penny stock, support for over the counter (OTC) stocks does not exist either. In other words, Robinhood has zero support for any tradable penny stocks on the over-the-counter stock market. If you are actively seeking to buy penny stocks unfortunately Robinhood is unable to help you.
What are penny stocks?
In simple terms, a penny stock is a highly speculative stock that tends to be very volatile and move sporadically. Any new findings on the web may drastically influence the pricing of a penny stock. Stocks under $1 tend to have tiny market caps, low prices and extreme volatility. Thus, there is a reason why penny stocks are not listed on two of the major stock exchanges in NASDAQ and NYSE. Most times penny stocks are major duds and a waste of time due to the unexpected risk of the company potentially going under. A new company issuing a penny stock and going under in a couple of months is a story told too often.
My best advice is to stay away from penny stocks, unless you have the risk tolerance and want to go against the grain. I tend to stray towards the more conservative side so I'd like to keep a roof over my head. In other words, my advice to you is that penny stocks are not worth the risk.