Photos app shows Modified Date whereas I need Original Date Taken

When you select an image to export from Photos, you have two choices from the Export menu:

1. Export 1 Photo
2. Export Unmodified Original for 1 Photo…

The second option does not change the creation or modified dates of the image as it was stored in Photos. That creation date corresponds to the EXIF DateTimeOriginal date within the image.

Confirmed on macOS Mojave 10.14.6 (18G2022)

Created and Modified dates are file system attributes. They have no correlation to the date the image inside the file was created. The image creation date is stored in metadata (EXIF data) embedded into the file image file.

The OS will display the EXIF data in a search for image files. It will also show that data in the image preview in Finder.

VikingOSX has provided a method to get the EXIF data correlated to the creation date in the file system. However, if there is no EXIF data embedded with the image, the file is just a file. It doesn't matter what is inside the wrapper.

Good point about the file format. The .png files created prior to July 2017 did not support an EXIF chunk, but those created afterwards (png 1.2 version 1.50 or later) can support EXIF chunks — if application support provides for it.

The third-party exiftool can extract the DateTimeOriginal:

exiftool -s3 -DateTimeOriginal some.jpg