“Jewish Rye Bread” refers to rye bread (with caraway seeds) that has been made in many Jewish communities.
     
“Jewish Rye Bread and Pumpernickel at Barr’s 317 N. Main” was printed in the Decatur (IL) Review on January 7, 1911. “Jewish rye bread” was printed in the Chicago (IL) Daily Tribune on August 23, 1913.
   
“You don’t have to be Jewish (to eat Levy’s Jewish Rye)” was a famous ad campaign from the 1960s.
   
   
Wikipedia: Jewish rye bread
Jewish rye bread refers to a type of rye bread commonly made in Jewish communities. Due to the diaspora of the Jews, there are several geographical variations of the bread. The bread is sometimes called sissel bread or cissel bread, as sissel means caraway seed in Yiddish.
           
Newspapers.com
7 January 1911, Decatur (IL) Review, “Local Notices,” pg. 8, col. 2:
Jewish Rye Bread and Pumpernickel at Barr’s 317 N. Main.
 
Newspapers.com
23 August 1913, Chicago (IL) Daily Tribune, “Smoke from a Bakery” by John L. Robinson,  pg. 6, col. 6: 
The smokestacks are not high enough to permit the smoke to go over the three story houses and as a result our houses are filled with smoke and the very strong odor of Jewish rye bread.
 
Google Books
January 1917, Bakers Review, pg. 88, col. 1:
Jewish Rye Bread
Please publish a recipe for genuine Jewish rye bread, and oblige, C. F., MD.
   
Newspapers.com
26 July 1917, Philadelphia (PA) Inquirer, “Male Help Wanted,” pg. 17, col. 1 classified ad:
BAKER—Second hand, exp. on Jewish rye bread. Halbert, 714 N. 2d st.
 
Newspapers.com
24 January 1920, Boston (MA) Globe, pg. 14, col. 8:
BOOST IN PAY
ABOUT 100 PERCENT
Reason Given for High Cost
of Jewish Rye Bread
 
Google Books
1 September 1921, Bakers’ Helper (Chicago, IL), “Jewish Bakery Goods” by Paul Richards, pg. 463, col. 1:
The method of making Jewish rye bread which is also known as Bohemian rye bread. varies in almost every bakery, and the rye flour is used in blends with more or less wheat flour.
 
Google Books
The Gentle People:
A Brooklyn Fable
By Irwin Shaw
New York, NY: Random House
1939  
Pg. 29:
MAGRUDER
On Jewish rye bread, Goodman?
 
OCLC WorldCat record
Any whitefish would give its all for Levy’s real Jewish rye.
Author: Robert Gage
Publisher: U.S.A. : [s.n., 1962]
Edition/Format:   Image : Graphic : Picture : Artwork reproduction : English
Summary:
Advertisement poster shows the remains of a “whitefish” with the bones picked clean between the head and tail fin, and a whitefish or tuna salad sandwich on Levy’s Jewish rye bread.
 
OCLC WorldCat record
You don’t have to be Jewish to love Levy’s real Jewish Rye.
Author: Howard Zieff
Publisher: [New York : s.n., 196-]
Edition/Format:   Image : Graphic : Picture : Artwork reproduction : English
Summary:
Advertisement poster shows an African American man with a sandwich made with Levy’s Jewish rye bread.
 
YouTube
Jewish Rye Bread
Mar 22, 2018
Nina In The Kitchen
The crispy crust, the tight chewy crumb, it’s all here! Jewish deli rye bread
Jewish Rye/ Eastern European Rye Bread
Yield: 2 large loaves, weighing 1 pound 13 ounces (834g)
*The caraway seeds are optional, but I highly recommend using them both crushed and whole.
Equipment: 1 large bowl greased, and two cookie sheets covered with parchment paper.
Oven temp 425°F or 218 ℃
 
In the bowl of a stand mixer with the dough hook attached; mix together:
 
2-3/4 cup of warm water (588g)
3 tablespoons of vegetable shortening
3 cups of medium or dark rye flour (309g). I used a fine cut rye flour, as opposed to a hearty coarse milled flour.
1 tablespoon plus 1 teaspoon of instant yeast
1 tablespoon of sugar
Mix on the lowest speed and slowly add:
 
3 to 3-1/2 cups (approximately) of bread flour, or all-purpose flour. Gradually add the flour and stop when the dough forms a ball. (360g)