Image size

Easiest option is to create a new document in Photoshop to the size you want (350x100px, 72 ppi).

Save your logo as an .ai native format and use File>Place in Photoshop to bring it in.

No reason to go through the efforts of extra file formats, etc.

Keep it simple.

"I would export the logo as PNG and then import it into Photoshop. But I need the logo in 350x100 pixels. "

You can also export using Save for Web, uncheck Clip to Artboard and specify export dimensions. 

Hi,

Indeed the Image Size option will only resize all the pixels, losing proportions, squeezing and streching them to the set size.

There is multiple way to achieve what you need, you can create an new PSD with a 350x100 pixels size and drag your svg/png file on the document, then adjust position/size to your liking.

Alternatively, you can use the crop tool on your PSD with a set size

You can also use the the canvas size option in the image menu, it will effectively crop pixels to the size you set:

Reagrds,