It probably doesn't. I tried searching but couldn't find one. But would be great if it does! Would help me remember so many new words. I hope somebody has figured out a pedagogical role of that symbol.
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This radical is called the 双耳旁 or 双二刀, due to it looking somewhat like an ear or the 刀 character. There are actually two radicals depending on whether it's placed to the left or right: 左耳刀 if on the left, 右耳刀 if on the right. The two radicals have different origins and different meanings.
The left version is derived from the 阜 (fù) character, meaning "mound" or "abundant". Characters with this radical are often related to mountains, hills etc, such as 陵 (hill), 险 (steep), 陆 (terrestrial).
The right version is derived from the 邑 (yì) character, meaning "city". Characters with this radical are often related to cities or human settlements, such as 都 (capital), 郊 (suburb), 郡 (commandery).
As far as I know, all radicals have meaning. The one you are talking about is 阝(fù) and called "Radical 170" (when used on the left, meaning mound or dam) or "Radical 163" (when used on the right, meaning city) while the Unicode dictionary says the radical means 'place'. Given the two examples you listed, it does relate to this meaning.
That "beta like" symbol "阝" is a radical (部首) called "阜" in Chinese. The pictogram (a very ancient form of Chinese character) of 阜 is , or (source of images: 中華民國教育部異體字字典). According to dictionary 說文解字 (compiled around the first century), "阜" means 小土山 (a mound or a hillock). So, the pictogram signifies a heap of gravel on the ground.
The pictogram for the character 附 ("attach") is (source: Chinese Etymology <- a great site!), which is comprised of three parts: a mound (i.e. the radical "阝"), a man "亻" and the character "寸" ("an inch", but a Chinese inch, of course). So, it uses the picture of a person leaning close to a mound to mean "attach".
The pictogram for the surname 陳 is . According to the dictionary 說文解字 again, the Chans got the surname 陳 because their ancestors initially resided in a place called 陳, and the major city in this place was 都於宛丘之側, i.e. next to a hillock named Yuan. That explains the radical "阝".