Reducing points but maintaining attributes from original shapefile

I have a shapefile with points but there are a lot of points and I want to reduce the amount.

I have tried "Points thinning" which automatically reduces the amount of points but it loses all the attributes/features/values from the original file (which I want to keep). In the 'Thinned Points' there are columns: 'Count', 'Mean', 'Minimum', 'Maximum', 'StdDE' which I don’t want.

How can I reduce points but maintain the attributes from the original file?