Vita is too weak to compete now.... if sony wanted to support a handheld, they would need to do a new PSP or Vita 2.0 or something.

Im no tech expert but i dont think it is possible at least not yet, maybe in a few years but by then PS5 will likely be out so that kinda defeats the whole purpose of a PS4 handheld.

I believe Sony is in business to make money, continue to grow their userbase, and create an ecosystem that can keep them viable for the future. So I have no doubt they will eventually attempt to connect their users to a mobile version of their platform. Whether they do it with PS4, or start fresh with PS5 is the only question in my eyes.

I think it will arrive in 2019 either in the form of a PS4, if Sony decides to build a PS4 Premium to make PS5 a truly next gen device. Or it could launch along side a weak PS5 in 2020 as part of the PS5 line of products.

The ultimate goal in business is to make money, and continually grow, to make more moeny. The ultimate way to make money right now, is to have people connected to your OS and Digital Store front 24/7, through every device they use through out their day. A new PS Portable, and even more so, the first PS Phone, would go a very long way towards that goal.

Sony should have learned a lot from PSP, PS Vita, Xperia Play (The half ass Phone that people confuse as a PlayStation Phone), and Switch. At this point they should know how to build a mobile PlayStation that will sell to a decent portion of their userbase, and make them a whole lot of money. If they don't they need different leadership.

What? The first Party Support is incredible.. 

Nah, I don't think so.

They'd be entering R&D around now and by the time it'd come out they'd be releasing the PS5 real soon, wich sort of defeats the purpose. The tech is also not nearly close enough to make a fully fledged PS4 portable, they'd have to go with a mobile chipset, wich again defeats the purpose.
Also Nintendo probably has some sort of exclusivity deal on the Tegra line with NVDIA, wich means Sony would not have access to the most powerful mobile chipline going forward either.
Unless they straight up go the Nintendo route and make their next console a hybrid, wich will probably sit inbetween the PS4 and the PS4 pro powerwise this just isn't technically feasable. And even then it's probably not a smart move.

It would sound more like a PSP3.

I don't think so

Nope I don't

I doubt it, unless Nintendo really continue to threaten their marketshare with what the Switch offers, then of course they'll consider it.

If they do though... I'll be damn pleased, got a few hundred ps4 games which would be amazing on a portable.

I don't think the technology is there yet to have the full power of a PS4 on mobile chips/hardware, and even if there was you wouldn't be seeing Nintendo Switch prices for it ($300), it would be a LOT more. 

The Switch has an X1 because that was literally the best mobile hardware available at the time the Switch was releasing that Nintendo could choose. X2 isn't available yet aside from some cars I think. Maybe a few years down the line as more powerful mobile hardware gets cheaper, but I don't think Sony could even try to do a PS4 portable at the moment without it costing a ton of money to the point where who's going to pay so much for it as opposed to just getting a PS4 for $250-300. And even then once that newer hardware might come out in a few years Nintendo will probably refresh the Switch for that as well with like a Tegra X2 version. 

But i'm also not sure that there will be any more portable-type things from Sony anyway. They seem set on just making sure their home consoles do well, and look at how great the PS4 is doing so far. They had a chance with the PS Vita and stopped giving a fuck about it completely after a while. Saying that though, I also wouldn't be surprised if they did either. I'm sure people said the same thing back during the 7th gen about how Microsoft and Sony weren't gonna copy the Wii, but eventually they did.