One of the primary segulos of lighting Chanukah lecht is to have children who are talmidei chachamim.
As Chazal say, בנר הרגיל חכמים תלמידי בנים לו הויין, "When one is accustomed to lighting Chanukah lecht, he will merit children talmidei chachamim."
The Gemara also says, לטלית זוכה בציצית הזהיר יין גרבי וממלא זוכה היום בקידוש הזהיר ,נאה, "When one is cautious with the mitzvah of tzitzis, he merits beautiful clothing. When one is cautious with kiddush on Shabbos, he merits having barrels of wine." These times the word הזהיר "When one is cautious" is used. Whereas, when discussing lighting Chanukah lecht, the Gemara says בנר הרגיל, when he is accustomed to lighting Chanukah lecht.
Feeling of Newness in Avodas Hashem
When we serve Hashem, there should always be a feeling of newness in our hearts, like we are performing this mitzvah for the first time. We shouldn't feel bored and disinterested. This can be hinted at in the words (Shabbos 21b) רגל שתכלה עד, "We light Chanukah lecht until the רגל, feelings of familiarity, cease, and every time we serve Hashem it is fresh and new."
Shem Mishmuel (5680) explains that the Gemara is hinting to us בנר הרגיל, one should become accustomed to serving Hashem with a נר, a fire of hislahavus. That is mesugal for children talmidei chachamim.
This can be hinted in the words (Tehillim 132:17) למשיחי נר ערכתי, "I have set up a lamp for My anointed/Moshiach." When mitzvos are performed with warmth, it brings Moshiach.
