Is there a way to create a shortcut in Eclipse that would jump the cursor to the nth column in the current row?

This is not a good practices but you can use this

Create Templates in eclipse Window -> Preferences -> Java -> Editor -> Templates -> New...

Name : 1
Pattern :${cursor}<give one space>

-

Name :2
Pattern :${cursor}<give two space>

.

.

.

Name : 26
Pattern :${cursor}<give 26 space>

As ridiculous as this requirement is, one Formatter preference setting can help you adhere to it. Open the Java Code Style > Formatter preferences (either workspace or project-level) and click Edit... to modify the active profile (or create a new one if you don't want this change to affect all code you write).

In the Formatter dialog, select the Indentation tab and then set Tab Policy to Spaces Only and Indentation size to 28.

With these settings, Tab will jump to the 28th column, and you can Backspace from there as needed.

Just be aware that this will pretty much ruin the ability to use the "format in bulk" feature of Eclipse (Right-click and choose Source > Format), because it will treat all indentation places with 28 spaces, which isn't what your mandated style seems to want. This only helps during typing.

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Even though this helps with such silly mandates, I repeat my comment above that the best advice here is to consider a new employer; if this is the kind of thing that is mandated, there are probably many other silly issues to deal with.