That looks like the EGR line.
https://www.rockauto.com/en/catalog/buick,1996,riviera,3.8l+v6+supercharged,1022038,exhaust+&+emission,egr+line,12319
https://www.rockauto.com/en/moreinfo.php?pk=8875168&cc=1022038&pt=12319&jsn=456&_nck=ZExt1ysfqhqWnq%2BEvUNdS3Txyey60IDtnjPWF5UU9J0BWQv7pvqZbkEUk86%2BAYIhFUNxSQbBt9FEuOpKheaSVujQQQ4UWses1J3xhfoGup4OBaCW%2FJQcT%2BbPC1FlQhMgLhaRLyX2e%2BYi7TPLWuWLj0E0b%2FEiVDWYpvOdO62a1nHIpVO6GSjTjFL9TPl6vdKIby5juj0tu%2BO9uWEd%2Fvf1S0obxGhSLovB1TmRPo%2FS3zTrw2RnZ22pCSZOto4QgC4j0sYJaTNoFUmzmO6rdggBHwNPdDD1PxThPhWW8xxzccqm4qmIzazqT9V7t5eTdoCyWXjTRQ0CcUR9N8zM8NKcOq3PQ%2FhJOCeS
If yours is in good shape, I would unbolt it and do one of two things. Either use some high temperature RTV, or, buy some exhaust gasket material and make a gasket.
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98 Riviera SC3800 All stock except gutted air box.
1970 Buick GS455 Stage1, TSP built 470BBB, 602HP/589TQ
Best MPH, 116.06 MPH, Best ET, 11.54
https://www.youtube.com/watch?v=UHCda-t_Jls
https://www.youtube.com/watch?v=sfT2tEO4XcU