I am unable to export an InDesign CC file (latest version) as a .jpg to an external SSD. I can export it as a .jpg to my internal drive just fine. This issue is exclusive to InDesign -- Photoshop, for example, exports .jpg files to the external volume just fine.
Also, exporting PDF files from InDesign to the external drive works fine.
I'm not sure why that's happening, but I've heard several people on this forum say that they like the quality of jpegs better when they start as InDesign PDFs converted to jpeg in Photoshop over jpegs exported directly from InDesign. Have you considered PDFing your InDesign work and using a Photoshop action or droplet to save jpegs to your external drive?