Is there any story that a Rakhasa has taken away Sita mata before surpanakha meet them, and later lord Rama and Shri Laxman fight with him and recover Sita mata?
Yes, the name of that demon is Viradha. This story is described in Ramayana, Aranya Kanda, Sarga 2.
अहम् वनम् इदम् दुर्गम् विराघो नाम राक्षसः || ३-२-१२
चरामि सायुधो नित्यम् ऋषि मांसानि भक्षयन् |
"I am a demon named Viradha and I will be on the rove in this impassable forest with weapon, always eating the flesh of sages... [3-2-12b-13a]
इयम् नारी वरारोहा मम भार्या भविष्यति || ३-२-१३
युवयोः पापयोः च अहम् पास्यामि रुधिरम् मृधे |
"This best waisted woman will be my wife, and I will drink your blood of you two sinful one in a fight with you... [3-2-13b-14a]
After that the demon captured Devi Seeta and then killed by Lord Rama and Lakshamana.