The question is what was keeping them occupied that month? January is a time of annual meteor showers so many sightings were explained away as that natural phenomena. The Quadrantids run from around Dec. 28 to about January 12th. It is one of three showers recognized as "dazzlers" producing a great show. See more at https://www.amsmeteors.org/meteor-showers/major-meteor-showers/.
Historically, however, in Project Blue Book there were some interesting sightings falling within the January 18-24th that might be worth a second look.
A great many reports came in from other countries. One from Hazuke, Japan for January 18 at 01200z was a air visual by military personnel for about 45 seconds. There was one object and it moved southward. The cover sheet report the sighting of a white object, appearing to have shape of project balloon at 40,000 feet moving fast with no smoke or contrail. It was noted that the object was moving opposite to the direction of the aircraft and was probably a balloon sighting.
Inside the report was a bit more details. The aircraft was on a mission for PROJECT 119-L, the aircraft crew Center 40 sighted object above the aircraft traveling in the opposite direction in the daylight. The object appeared to move, seeming 1000 ft above the aircraft and then about 5000 ft above them. One witness described the object as looking the way a weather balloon looked to the eye at 40,000 feet. (It should be noted he not use the terms as a descriptive but as a comparative). Making comments were crew members commander Owen, 1st Lt. Richard A. Wilder. A check was made a no weather balloon releases could be found and the weather at the time was clear.
North Plate, Nebraska was only one of numerous January 1956 cases. A civilian observer on the ground saw 1 object descending to the west. It was on the cover sheet described as "round in middle rods sticking out, size of a baseball, silver color, yellow and green colors coming out of the top. No sound."
Comments were short and sweet: " Duration and motion to the west as well as distorted appearance given object indicate observation was astronomical body. Any planet on elliptic from 22h to 24 h with magnitude of -1 would conform to characteristics of this observation. Venus was at 22h 10', magnitude -3.4."
Inside the report there was, as so often is the case, additional information. The object was 45 degrees off the horizon, it "spinned out of sight" and "headed west at slow speed and was red on both ends bright in center" and the observer had used binoculars to view the object.
The sighting time was listed as 18/2345z (N) for two hours.
Stroud, Oklahoma, 5-10 miles south of Stroud, on January 19, 1956 at 1651z (daylight) an F84f pilot observed four objects moving east for about 3-5 seconds. He observed four objects the size of a bushel basket at arm's length that were a brilliant emerald green and with it 3 smaller objects white and silver. He tried to establish a fiz on radar but was unsuccessful and he noted he had never seen any meteor as bright or as green as the object he saw.
They followed a straight and level flight heading east.
The explanation was that he had observed a rare daylight meteor, a transient celestial body, true but perfectly natural occurrence.
January 24, 1956 a report came in that across Afghanistan objects were being seen. Objects saucer shaped and square were reported in the skies in Durbaba, Sassubi and in Herat Province. There was a story that one had landed near the town of Takala and was going to be taken to Kabul. Object descriptions were : 15 feet in circumference, metal, small, thick glass windows around leading edge and saucer shaped.
From Oroszlany, Hungrary from January (no day listed) were reports of objcets seen between 2230 and 2300 by civilians on the ground for 6 minutes as they headed east. They were described as dimly lit objects moving slowly west to east, triangular in shape with a bright spot in the center. The estimated altitude was 3000 meters.
Most odd was that these objects seemed rigidly connected and rotated slowly around the center. No noise, exhaust or trail was seen. It was classed as insufficient data with the remarks that it was possibly aircraft or gliders. Inside was the additional information that the objects formed a square on a horizontal plane - distance between the objects was unknown but that they rotated as if "rigidly connected."
The weather at the time was listed as cloudless, 100% visibility and windless.
Yesterday I was interviewed by an ABC news affiliate in Oklahoma (KOCO) about my UFO books, research, and the stories I uncovered. The setting could not have been better, the "Office of Clark Kent" in the Spirit of America Route 66 Museum in Stroud, Oklahoma. Thanks to Museum owner and director, Steve Brant. 
