Yes. Exchanges call these "weekly options series" or "Weeklys”. In addition to previously listed index weekly options series, the exchanges participate in an approved program that allows trading in some equity and ETF weekly options. Weekly option series are listed on a Thursday and, in most cases, expire the following Friday. Each exchange can list weekly options series on a limited number of classes. Become fully familiar with the contract specifications of any option product you trade by visiting the exchange website where that contract trades.
OCC publishes this list of newly added and newly delisted Weekly Option Products that have been processed through OCC's internal series listing application. These series are in the weekly program for the next eligible weekly expiration.