Prison of the Hated Pretender is an introductory adventure for 4-6 characters levels 0-1. Originally published on the Dungeon of Signs blog, it is a short drop-in location-based adventure with a couple of interesting puzzles, a lack of "book" monsters, implacable foes with an obvious weakness, and a very weird roleplaying opportunity. The new 2020 edition republished by Hydra Collective adds suggested guidance for new Dungeonmasters who grew up with 5th edition and don't know how old-school works. Stats for both BECMI and 5th edition, and setting neutral (though there are some implied things about the history of the world).
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fatmessiah has played this adventure and would recommend it.
I've run this twice, and the players had a great time despite one group being absolute novices and one being veterans of the psychic wars. It's got the wonderful weirdness of very early D&D -- the sort that was scraped off in the '80s by the TSR focus on ease-of-play and corporate blandness -- but incorporating 4 decades of subsequent experience in how RPGs should properly work.