The 1. Fallschirmjäger-Division was formed from 7. Flieger-Division in April 1943 and was sent to Avignon, France, as a reserve force for rest and refitting. Following the Allied landings on Sicily it was sent to Italy with Fallschirm-Jäger-Regiment 3 making a parachute jump into Catania on Sicily on 12 July to secure the airport. It was forced to make a fighting withdrawal along with the rest of the German forces and it was the last unit to leave on 17 August.
Fallschirm-Jäger-Regiment 4 was among the German units fighting the landings of the US Fifth Army at Salerno in September and was joined by the rest of the division for the withdrawal north.

The division famously fought at Monte Cassino which formed a part of the German Gustav Line from January to May 1944, stubbornly resisting the Allied forces from the bombed monastery earning the nickname "Green Devils" before withdrawing further north.
The British Field Marshal Harold Alexander wrote in a memorandum to Winston Churchill in March 1944:

The destruction caused in Cassino to roads and movement by bombing was so terrific that the employment of tanks or any other fighting vehicles has been seriously hampered.The tenacity of these German paratroops is quite remarkable,considering they were subjected to the whole Mediterranean Air Force plus the better part of 800 guns under greatest concentration of firepower which has ever been put down and lasting for six hours.I doubt if there are any other troops in the world who could have stood up to it and then gone on fighting with the ferocity they have.

Known war crimes
This unit was one of those singled out in exhibit UK-66, the British report on "German reprisals for Partisan activities in Italy" at the International Military Tribunal (IMT) war crimes trial at Nuremberg:

Evidence has been found to show that a large number of the atrocities in Italy was committed by the Hermann Goering Parachute Panzer Division. Notable offenders also were 1 Paraschute Division, 16 SS Panzer Grenadier Division and 114 Light Division. (1)

Commanders

General der Fallschirmtruppe Richard Heidrich (1 May 1943 - 4 Apr 1944)
Generalmajor Hans Korte (4 Jan 1944 - 21 Feb 1944)
General der Fallschirmtruppe Richard Heidrich (21 Feb 1944 - 17 Nov 1944)
Generalmajor Karl-Lothar Schulz (18 Nov 1944 - 2 May 1945)

Area of operations

France (May 1943 - July 1943)
Sicily (July 1943 - Sep 1943)
Italy (Sep 1943 - May 1945)

Order of battle

HQ
- Staff
- Motorcycle Platoon
- Military POlice Detachment (mot)
1. Fallschirmjäger Regiment
- Staff
- Signals Platoon
- Bicycle Platoon
- Pioneer Platoon
- 3 x Fallschirmjäger Battalion
-- Staff
-- Signals Platoon
-- 3 x Company
-- Heavy Company
3. Fallschirmjäger Regiment
- Staff
- Signals Platoon
- Bicycle Platoon
- Pioneer Platoon
- 3 x Fallschirmjäger Battalion
-- Staff
-- Signals Platoon
-- 3 x Company
-- Heavy Company
4. Fallschirmjäger Regiment
- Staff
- Signals Platoon
- Bicycle Platoon
- Pioneer Platoon
- 3 x Fallschirmjäger Battalion
-- Staff
-- Signals Platoon
-- 3 x Company
-- Heavy Company
13. Fallschirmjäger Nebelwerfer Company
14. Fallschirmjäger Panzerjäger Company
1 / 1. Fallschirmjäger Artillery Regiment
- Staff
- Staff Battery
- Signals Platoon
- 3 x Battery
- Supply Column
1. Fallschirmjäger Panzerjäger Battalion
- Staff
- Signals Platoon
- 3 x Battery
1. Fallschirmjäger Pioneer Battalion
- Staff
- Signals Platoon
- 4 x Company
1. Fallschirmjäger Flak Battalion
- Staff
- Signals Platoon (mot)
- 3 x Battery
- 2 x Self propelled Battery
- Supply Column
1. Fallschirmjäger Medical Battalion
- 2 x Company
- Field Hospital
- 3 x Ambulance Company
Supply Troops

Notable members

Herbert Fries (Credited with destroying 20 tanks 21-24 May 1944 in a fortified Pantherturm)
Johannes-Matthias Hönscheid (the only war correspondent, kriegsberichter, to recieve the Knight's Cross)
Harald Quandt (stepson of Reichsminister Dr. Josef Goebbels)
Alfred Schwarzmann (winner of three Olympic gold medals in gymnastics and member of the "Hall of Fame des deutschen Sports")

Insignia

The "Fallschirm-Jäger Rgt. 1" cuff title was authorized for Fallschirm-Jäger-Regiment 1 on 19 August 1939.

Photo © Ruptured Duck

Standard of the 3. Batallion of Fallschirmjäger-Regiment 1

(Courtesy of Wikimedia)

Standard of I./Fallschirmjäger-Reigment 1, dating back to the Landespolizeigruppe Wecke z.b.V. and Regiment General Göring days

(Courtesy of Wikimedia)

In fiction

The 1987 board game "Thunder at Cassino" designed by Courtney F. Allen and published by Avalon Hill covers the fighting around Monte Cassino.

Footnotes

1. UK-66, the British report on "German reprisals for Partisan activities in Italy" at the International Military Tribunal (IMT).

Sources used

Chris Ellis - 7th Flieger Division: Student's Fallschirmjäger Elite
William Fowler - The Secret war in Italy: Special forces, partisans and covert operations 1943-45
James Lucas - Storming Eagles: German Airborne forces in World War II
Gordon Williamson & Thomas McGuirl - German military cuffbands 1784-present
Unit insignia illustration courtesy of Wikimedia

Reference material on this unit

Edgar Alcidi - Along the Neva: German Paratroops of the 1st Battalion 3rd Fallschirmjäger Regiment on the Russian Front September-November 1941
Ben Christensen - The 1. Fallschirmjäger Division in WWII (2 vol)
Chris Ellis - 7th Flieger Division: Student's Fallschirmjäger Elite
G. Klitzing - Geschichte des Fsch.MG.Btl. und des Fsch.Gr.Werferbtl. 1 1940-1945
Alfred Meyer - Chronik des Fallschirm-Artillerie-Regiments 1 1938-1945
Klaus Peters - Fallschirmjäger-Regiment 3 (2 vol)
Gottfried Zelfel - Chronik der Fallschirm-Panzer-Jäger-Abteilung 1 1939-1945