Can I make a paid app on playstore free on fdroid ?

Sure , indeed there are some foss app that are the same as you described

True, but I think typically the Playstore version isn't always from the official maintainers and I'd consider it less trustworthy, even if free (unless the devs link to the playstore page on github/gitlab/codeberg/whatever).
- The examples I know are officially published by their orginial developers
- the play store version isn't as trustworthy even if the original devs published it there, since google forced all developers a few years ago to hand over their signing keys. the signature is how you know the app wasn't modified by anyone, and that actually the developer released the apk

Yes, a lot of developers have done this. Many examples have been posted on this thread (OsmAnd, Conversations, Davx5) - Mindustry is another example. free on f-droid (and Google store too I think), but $10 on Steam.

If you own the copyright then yes this is 100% legal.

There are already apps that are like this. They usually add a couple features to the paid release so that people feel like they are getting something extra for the money. The good ones will eventually move those features to the open release eventually. However, this incentivizes keeping part of the app closed source so that nobody can just rename and re-release the paid version.

It is 100% up to you for how to handle these tradeoffs. Personally, I think so long as you are principled and ready for some criticism - and can handle it gracefully - getting paid for work that builds your open source app is a very good idea. We don't all have the luxury of maintaining high quality unpaid side projects!

An alternative is to have both be the same and have one just be for people who want to contribute monetarily to your efforts or have the convenience of using their preferred store (if playstore is their preferred store). I think that's sort of what Mindustry does (a foss game). It is available for 10€ on Steam, but also available for free on itch, with the steam version just having the benefit of being a steam game and having steam achievements. I guess ethically all is fine if you make clear that the game is also available for free from another place.
If you don't own the copyright and its libre software, this is 100% legal too

Conversations, an XMPP chat app, does exactly this.

Free software is a matter of liberty, not price. It is perfectly legal and ethical to sell free software. Keep in mind if you're using third party code (whether it's libraries or external contributions to your application) you must abide by the terms of whatever license it is under, this is whether it's paid or gratis.

It's even perfectly legal to fork an existing free software project and sell it on the play store, although whether that is ethical or not is up for debate - depending on what efforts you put into your fork before selling it, an orthodox Stallmanist might have no problem with it but the original developer(s) of that code may perceive this as "theft." Keep in mind you must abide by the terms of whatever license the project is under, so if it is a copyleft license like the GNU GPL you must either provide corresponding source code or an offer for such.

Some just do it to make some extra money and save for convenience. Krita is free to download and install yourself. It's 10 bucks if you want to get it on Steam. It's perfectly within their right. Especially in KDE's instance.

Free and Open Source developers have often a hard time to earn money for their work. Having it for 10 Euros/Dollars on Steam is an easy way for them to earn money and for users to support the software they like. I honestly wish more Free Software would come to Steam for little support money. I like the universal simple account to pay through Steam with Steam cards and don't need another account or bank transfer for each project. It's a small one time fee.

Yes, search for it

As long as you are the legal owner of the code, I don't see why you couldn't.

For example, DAVx⁵ (F-Droid, Google Play)

I'd see it as a tradeoff between the convenience of silent updates of Google Play and incentivizing people to go for F-Droid.

Is this your app? If yes then sure, it’s your app you can do whatever you want with it. ~~If you are still morally troubled then just offer a free apk for those who don’t want to pay but also don’t want fdroid (for whatever reason there is, I don’t know of any).~~

You can download an APK from the F-Droid website

I can think of a few apps that do this. It is certainly possible. I think it is ethical; if someone is not participating in the open source community, they miss out on the benefits. I think most people involved do contribute in some way. If someone just wants to use Google for the benefit of ease and discoverability, then they can pay for it. You're still offering an ad-free app (presumably) and adding use value. It's perfectly reasonable to suppliment the cost of development in is way.

If you have the rights to publish the software, then you can do that. Why would it be illegal or not ethical? If you have the rights to, then you can even publish your software with different license on both "platforms", if you want to.

Do you want publish your own software or do you think of taking an existing Open Source software and sell it on PlayStore? It would be good to know what your goal is. Or is this a question of curiosity?

Would be my software
- Then you can do whatever you want with it. You can publish it under different licenses or charge money on one platform and not charge any money on another. Its all up to you and its legally right and ethical. Some people don't like that you charge money for an Open Source program, but that is their decision. Its totally okay to charge money for something you created. Don't let people dictate you how to publish and sell your own software. If someone does not like paying and supporting you, you can always point to Fdroid or the source code. Absolutely ethical.

Why would it be illegal, or unethical? I don't really see any reason.

I thought because some people wouldn't know about the app and may think they have to pay
- Is it against playstore rules to say in the description they can get it for free elsewhere? I do see how it could be or feel unethical, if people aren't aware.

Label the Play Store version as "Pro" but don't actually change anything. It'll have a placebo-like effect and make people feel better about spending money.

It's perfectly legal but personally, I would not find this really ethical: a lot of people don't know F-Droid and if they find your application directly in the Play Store, they won't know they can have it, the exact same application, for free but elsewhere.

I prefere one of those solutions:

The ability to send a donation, it's a very common thing.
Having the same application twice on the Play Store, one for free and one with a fixed price (I don't remember which app do this but I saw it once).

Of course this is my point of view, everyone has its own vision of what is ethical or not. Do not take my comment as the absolute truth!