I've been searching the web for this over the past week but all I could find was just a conclusion.
First, let's see this. I'm pretty sure you know about this quote.
“I did begin a story placed about 100 years after the Downfall [of
Mordor], but it proved both sinister and depressing. Since we are
dealing with Men it is inevitable that we should be concerned with the
most regrettable feature of their nature: their quick satiety with
good. So that the people of Gondor in times of peace, justice and
prosperity, would become discontented and restless – while the dynasts
descended from Aragorn would become just kings and governors – like
Denethor or worse. I found that even so early there was an outcrop of
revolutionary plots, about a centre of secret Satanistic religion;
while Gondorian boys were playing at being Orcs and going round doing
damage. I could have written a ‘thriller' about the plot and its
discovery and overthrow -- but it would be just that. Not worth
doing." - J. R. R. Tolkien, Letter 256
Tolkien had written 13 pages of this story and decided to let it go because it turned darker than he intended to made in the first place and he found it very depressing. This doesn't mean he didn't work on any sketches but even if he did, they are not publicly available at the moment.
It is known that Christopher Tolkien gathered, edited and published many of his father's unfinished/finished works and I can only speculate about a sketch that was designed for the era that is explained in The New Shadow.
But if you are interested in Tolkien's other sketches like the early designs of Middle-earth and some animal descriptions he himself designed, I recommend you to check these links: