Unfortunately as odd and illogical as it sounds USCIS will still take the position that such activity, whether paid or not constitutes "unlawful employment".
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Yes. If it is your hobby, you can do that.
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In my opinion, as long as there is no "renumeration" of any kind, whether old fashioned money exchanges hands or whether in kind benefits I believe you ought to be ok. Obviously the safest thing to do is not do it at all. Also make sure that this not violate any of your current employer's employee handbook rules and regulations. You do not want to loose your H-1B for an innocent hobby you like to engage in.
I think there are two issues for you to examine : 1) Would the publishing of the free app come up during any application process in any way, shape, or form?; 2) If the answer to issue one is "yes" then you would have to determine how comfortable you are explaining that the app is free and that you made no money from it whatsoever. USCIS has the tendency to assume facts that may or may not be accurate and this could cause an issue later on for you. My advice is that I do not see anything wrong with what you described but to proceed with caution because USCIS may not share the same opinion.