Notes: All timings are represented in 24+ hour notation in local time of Columbus, United States with DST adjustment (if applicable).
Hours past midnight are higher than 24:00 and fall on next day. In Panchang day starts and ends with sunrise.
Devi Aparajita is worshipped on the day of Vijayadashami. The best time to perform Aparajita Puja is Aparahna (अपराह्ण) time as per Hindu division of the time. Goddess Aparajita is worshipped for the victory.
It is believed that Lord Rama worshipped Goddess Aparajita on Vijaya Dashami day before His departure for Lanka to defeat Demon Ravana. Before taking any journey, Goddess Aparajita is worshipped as Her blessings help to fulfill the purpose of the journey and make the journey safe.
Goddess Aparajita Puja Mantra -
इमां पूजां मयां देवि यथाशक्ति निवेदिताम्।
रक्षार्थं तु समादाय व्रजस्व स्थानमुत्तमम्॥
Meaning - O Devi, after accepting my Puja, which was done as per my capacities for the victory, please depart for your place.
हारेण तु विचित्रेण भास्वत्कनकमेखला।
अपराजिता भद्ररता करोतु विजयं मम॥
Meaning - O Aparajita Devi! Who shines with multi-colored necklace and adorned with golden belt, please bestow victory on me.