the press; in the newspapers
Refers to the medium of newspapers as a public forum; often used in phrases like 新聞紙上をにぎわす (to be much talked about in the newspapers) or 新聞紙上で発表する (to announce in the newspapers).
The incident was much talked about in the newspapers.
The company president apologized in the newspapers.
新聞 is the general word for 'newspaper' as a physical object or institution. 新聞紙上 specifically emphasizes the newspaper as a medium or forum for public discourse.
紙上 means 'on paper' or 'in print' and can refer to any printed medium. 新聞紙上 narrows it to newspapers specifically.
Compound of 新聞 (newspaper) + 紙上 (on paper, in print). The reading しじょう for 紙上 is standard in this context.