Photoshop don't export to 300 dpi

As already mentioned, Export As strips all PPI metadata. Save As retains it.

That being said, it is possible to "inject" the 300 PPI metadata value into JPEG files generated via Export As (either using 3rd party software such as ExifTool or via JavaScript):

I hope the the comments above answer why you are not getting the desired 300 dpi when you output your file using the Export function. I want to reiterate that jpgs are not the best file for print. If you are importing your files into InDesign, jpgs will not give you the best image quality for color.

What is your print workflow? I get really good results importing my native Photoshop files into InDesign and the best color options for my images.

Let us know if you have any questions,

Michelle

Why are you using a JPG for print? How are you using this JPG once it leaves PSD?

Don't use Export - it's for Web images at a low resolution

Set image size and ppi as required

Go to "save as" and set the format to Jpeg if that’s what you want

you may need to check legacy "Save As" file handling Preference

a note on Jpeg:

JPEG files have compression applied, changing resolution or cropping and re-saving enhances the compression artefacts - this means that Jpeg is only really suitable for final file delivery/transfer - once size and resolution (and any sharpening) have been completed. 

Jpeg is not OK for editing or archiving or for any file that may need to be resaved, resized or cropped down the line.

Jpeg is the worst possible format if you want to keep high quality - you should always archive a copy of your original, with adjustment layers intact - if that’s how you work.

Jpeg compression (at any setting*) really is "lossy”, irreversible and cumulative, so should ONLY be used only for final delivery AFTER resizing & cropping to the FINAL size and crop.

Why? Any edits to size or crop, or even just re-saving a Jpeg file means further compression, potentially that’s very damaging.

The jpeg damage is not always immediately apparent, which is perhaps why it's still widely used - however, the compression will soon cause issues if you do further work and save again. That’s when you’ll see a jpeg with some real issues.

*don’t imagine that selecting maximum quality for your Jpeg is preserving the original data, it’s still compressing a lot which discards information.

I hope this helps
neil barstow, colourmanagement net - adobe forum volunteer - co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management 

Yes, I understood the question. Is the solution not clear?

Export is only for web files. The ppi value is not relevant to web use, so it is ignored. Yes, "export" is a very bad name for this function. You need to use SAVE A COPY (SAVE AS in older versions of Photoshop) to save for print.