Marlin Model 444s were discontinued in 2012, after Remington ditched the existing tooling, fired all of the Marlin craftsmen, completely botched production on new tooling in Ilion NY, and put out some HORRIBLE rifles that required extensive repairs and many, many full refunds.
Marlin 444s used a 1:38" twist 'Micro-Groove' barrel, from 1963 to mid-year 1998. From mid-1998 until discontinuation, all barrels were "Ballard" rifled with a 1:20" twist.
Remington announced reintroduction of the Model 444 in 2014 (twice) ... and 2015 (thrice) ... and 2016 (thrice) ... and 2017 (once - "shipping 2Q 2017"). So far, only three pre-production samples have been seen, with about 50 rifles reported to have shipped to distributors in 2014, but immediately recalled with no reason given. None have made it 'into the wild'.
It might still happen, but don't get your hopes up. Remington has been announcing new Model 444s for a couple months shy of four years now.
So...
If you want a 1:20" twist .444 Marlin, the options are limited to used rifles.
For Marlin: 1998-2008 are the acceptable years for Marlin 444s. Don't go newer than 2008. (Quality was falling, even before Remington really screwed the pooch.) 2007 and 2008 are considered by 444 aficionados to be the cream of the crop for a 'modern 444'.
Personally, I have found the 2007 and 2008s to be the quality and performance pinnacle for the model, as well -- even including the Micro-Groove ("MG") years. None were bad years. It's just that Marlin finally got it almost perfect, just before the slump.
If you can get by with a single shot, a used H&R Handi-Rifle (also discontinued by Remington ... in 2015?) in .444 Marlin will have a 'Ballard' 1:20" twist barrel.
For a new single shot, CVA offers a couple models that have 1:20" twist rates.
Winchester used several twist rates for .444 Marlin barrels, over the years. Again, you have to look for a used rifle. But the twist rates were adequate (between 1:24" and 1:30").