I have Windows 8 on my laptop and the jumplist for putty has always worked just fine. After installing Putty on my desktop (Win 10) the jumplists do not show up when I right-click the taskbar icon, Putty v0.65.
After scouring the internet, apparently a fix was provided in version 0.66. So I uninstalled 0.65 and installed 0.66... no help, same issue. some comments on a similar question to this actually said they had better luck with the development version, so I uninstalled 0.66 and installed the 11/30/2015 version of Putty. I have unpinned and re-pinned as well as deleted my saved sessions and recreated them. I even tried to clean registry entrys with ccleaner after uninstalling and before installing. I currently have 2 saved sessions and this is what my right-click taskbar context menu looks like (start menu jump list is exactly the same):
P.S. I have visited this question and tried it's solutions. However, I was not able to comment due to my limited reputation, so I had to create my own question.