Removing intersect or overlap of points in the same vector layer

Question

Is there anyway to remove the intercept part of the vector points?

P.S. Please ignore the red circle, it's not a polygon, it is a hand drawn by me to show the error part
So far I've done: "Select by location" and Geometries Checking. But there isn't a way to work.

BERA · Accepted Answer

One way of doing it, which could work:

DBscan Clustering to give each cluster of nearby points a cluster ID, adjust maximum distance:

Delete duplicates by attribute by cluster ID:

Removing intersect or overlap of points in the same vector layer

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