〜つつ（も）
While doing; even though (written style)machine translation
FormationVerb ます-form (drop ます) + つつ／つつも
〜つつ is a written form with two meanings parallel to ながら. Meaning 1 — two simultaneous actions: 景色を楽しみつつ歩く (walking while enjoying the scenery). Meaning 2 — concession "even though…," usually in the form つつも: 悪いと知りつつも、やってしまった (even though I knew it was wrong, I went and did it).
The only connection: ます-form minus ます + つつ（も）. Like ながらも, the concessive meaning often pairs with cognition verbs 知る・思う・言う; however, つつ cannot attach to adjectives or nouns — that is something ながらも can do that つつ cannot.
On register: つつ is formal, leaning toward books, essays, and news; in everyday conversation Japanese people use ながら（も）. Finally, don't confuse it with 〜つつある ("gradually …ing") — they look alike but are entirely different patterns; that one describes a change in progress.
Examples
体によくないと思いつつも、夜遅くまでスマホを見てしまいます。
Even though I know it's bad for my health, I keep looking at my phone late into the night.
景色を楽しみつつ、山道をゆっくり歩きました。
I walked slowly along the mountain path, enjoying the scenery as I went.
いけないと知りつつ、授業中に寝てしまいました。
Even though I knew I shouldn't, I fell asleep in class.