You're gonna be disappointed then because I and a lot of others can tell you it's not happening. There is no place for a dedicated handheld in this market, Sony did good on ditching the Vita (from their perspective) as there is so little to gain from making the effort of not having a catastrophically selling handheld (WW)
Even Nintendo is just doing ok at best in the west, can't imagine what Sony would do next generation with another handheld.
I'd seriously disagree with the idea that there's no place for handhelds in this market. I think the main problems with the Vita were cost, proprietary technology, and a visible lack of support.
The Vita was basically a $350 base investment when it launched, between the system, memory card, a game, and tax. That's a steep price to ask for anything, much less a secondary gaming device. The price of memory cards was also so high because they were proprietary, which was a decent effort on Sony's part to prevent the rampant piracy on PSP from repeating itself, but it obviously had its flaws. Between that and the weird charger that was fixed with the Vita 2000, it didn't exactly lead to glowing reviews. And topping that with the fact that Sony's been largely ignoring the system since it launched, it's easy to see why it didn't do too well.
Now if Sony were to release a new handheld in a few years, work with someone like Nvidia and get the newest Tegra chipset in the system, they could have a powerful, yet not too expensive device comprised of parts for mobile phones, but with dedicated controls and a solid form factor, use MicroSD for storage, and use USB type C for charging/data sync. Using Tegra would also be beneficial because they wouldn't be dumping a lot of time and money into R&D to develop their own chipset.
The only thing left to do is get games on it, and Sony could easily do that by working with the indies and small studios they have close ties to, and find developers interested in remaking or continuing franchises they own but aren't doing anything with, whether they're old PSP franchises (Patapon, LocoRoco), or from the PS1/2 (PaRappa, Jak and Daxter, MediEvil). Sony doesn't need to put much of their own man-power into the device, as long as it gets PlayStation games.
Something like that would definitely catch on more than the Vita, and could actually be a viable platform outside of Japan, if marketed correctly. The Vita's failure is on nobody but Sony, and they're the only ones that could keep this from happening again. Fans of the platform have been so vocal about how good it is, and indie devs have kept it afloat while Sony's done absolutely nothing for it on the software side.
I want it too. Being able to play my older PC games on the go? That's a dream come true.