One oddity about comics is how seldom we encounter relatives of superheroes, especially siblings. Kal-El had no brothers or sisters; neither did Bruce Wayne, Dick Grayson, Peter Parker, Barry Allen, Jimmy Olsen... it might save some time to mention characters that we know did actually have siblings in the Silver Age: Lois Lane (sister Lucy), Scott Summers (brother Alex), Sue Storm (brother Johnny), Quicksilver (sister Scarlett Witch) and Hal Jordan (brothers Jim and Jack).
The first three mentioned had a fair number of appearances in the Silver Age. Johnny Storm was the Human Torch, and he appeared in both Fantastic Four and Strange Tales. Havok appeared in the last dozen or so issues of the Silver Age X-Men. Lucy Lane became the permanent love interest for Jimmy Olsen during the Silver Age.
Jim Jordan, on the other hand, appeared in only a few issues of Green Lantern, becoming more or less an annual character. The interesting part of these stories was that Sue Williams became convinced because of an odd set of circumstances, that Jim was secretly Green Lantern. In her first appearance with Jim (GL #9), Sue's a magazine reporter determined to get the scoop on Green Lantern's secret identity. By the end of that story she's convinced (wrongly as we know) that Jim is actually GL.
Hal's brothers next appear in GL #14. By now, Sue's introduced as Jim's girlfriend. She discovers an old green lantern in Jim's hotel room and is convinced that it is the famed lamp that gives GL his powers. Earlier, Jim and Hal have accidentally switched rings, so he does briefly have super abilities, which just serves to confirm Sue's suspicions.
The Jordan brothers next appear in GL #22's Dual Masquerade of the Jordan Brothers. Red Peters, a criminal has just escaped from jail. As it happens, Jack Jordan was the prosecutor who sent him to jail, while Uncle Jeremiah Jordan was the judge who sentenced him, and Green Lantern captured him. Since Sue has written about her suspicions that Jim is secretly GL, she is concerned that Red will be gunning for the Jordans at Uncle Jeremiah's upcoming birthday party.
In one of those "convenient for the plot" moments, the birthday party turns out to feature a masquerade, although in a sloppy bit of art, Jim Jordan and Red Peters seem to be the only ones wearing a disguise. Hal decides to play along with his brother's impersonation of GL in the hopes that Peters will be scared away.
In GL #31, the Jordan Brothers return. This time Jim is about to be married to Sue, but then a villain appears with a bizarre threat:
Once again, Green Lantern comes to the rescue, and once again, circumstances conspire to convince Sue that her husband (they marry in the last panel of the story) is secretly Green Lantern.
Jim returns again in GL #44. He has started a new career as an image maker, and his first client is another uncle, this time millionaire Titus Jordan. Sue has enrolled Uncle Titus in a scheme to establish once and for all that Jim is secretly Green Lantern. Uncle Titus wants Hal to pretend to be a super-criminal named the Bottler (sheesh, what a scary name for a villain). But the real Bottler shows up and Hal, the real Green Lantern, once again saves the day, but leaves Sue more convinced than ever that her husband is secretly the Emerald Gladiator.
In GL #53, Hal babysits his new nephew, Howard Jordan, the son of Sue and Jim, while the young couple attends a play. But the theatre is robbed and when GL shows up to defeat the crooks, Sue is even more convinced than ever that he is secretly her husband.
Jim, Sue and Howard make a cameo appearance in GL #63. The whole family gets together for their final appearance in GL #71. In this story, they meet up with Doug Jordan, who somehow is a hippie from Tennessee. Sue is convinced Doug is up to no good, so she insists that Jim take care of him as GL. But Doug (who is indeed a bad 'un), konks Jim and takes him to a motorcycle gang he's trying to join. Fortunately the real GL arrives in time to save him. In the end, Jim extracts a promise from GL to come to the party to prove to his wife he's not the superhero she thinks he is. GL agrees, but only because he's already going to the party as Hal, and thus Sue remains convinced that her husband is the ring-wielder.