Is there a way to make vscode line number field smaller width?

You can’t change the size of this column.

Actually there are three columns:

• left of the linenumber is the column called glyphMargin, the place to set debugging breakpoints (red dot). (When you edit settings, the column displays a pen when you point on the line as seen in the screenshots below)
• the line number itself
• right of it you can fold/unfold your code.

If all three are active, it looks like this (settings) or a like above (code)

To save space you can

• switch off the display of line numbers:

  "editor.lineNumbers": "off"
  

  

• switch off the code folding feature:

  "editor.folding": false
  

  

• if you don’t use the debugger, disable the glyphMargin:

  "editor.glyphMargin": false
  

  

This is probably not what you want, but if you don’t use code folding or the debugger or don’t need linenumbers, you can at least save a little bit of space.
To change these settings press ctrl, or click on the menu file/preferences/settings.