SAVING A PNG FILE IN PHOTOSHOP AND CHANGING THE DPI AT THE TIME OF SAVING PNG

When you so Save for Web (File>Export>save for Web) or Export As (File>Export>Export As) you can change the dimensions of the exported file, but not the dpi. That can be changed under Image Size (Image>Image Size...)

If you need a copy you can duplicate your file (Image>duplicate) , then you can go to Image>Image Size to change the dpi

Hope that helps!
cheers,
mark

Hello

Is it in Photoshop CC "without any number after the CC?"

It will be important, as some of the answers might not be relevant for that version.

Save/Save as do not give you a DPI option.

Both Export as (recent versions) of Save for web do not offer a DPI option, but an image size in pixels or percents.

Scripts>Image Processor has no PNG option.

One solution that has the option is the third party (but free) Image Processor Pro 

https://sourceforge.net/projects/ps-scripts/files/Image%20Processor%20Pro/v3_2%20betas/