aspg-21-3470-1791475510 20261008160510 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 4 Layla Esmet Jalil Department of Mathematics, College of Science University of Kirkuk -Kirkuk, Iraq Mohammad El-Ityan Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan Rafid Habib Buti Department of Mathematics and Computer Applications, College of Science, Al Muthanna University, Iraq This paper investigates the 𝔓𝕞ℵ operator, constructed from the Neutrosophic 𝓆-Poisson distribution series. The study examines this operator within the realm of geometric function theory, focusing on key characteristics such as coefficient bounds, growth and distortion behavior, and the determination of convexity and star likeness radii. Additionally, the paper explores the weighted and arithmetic means of functions associated with this operator and analyzes its closure properties under the Hadamard product. 2025 230 239 3470 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250419 https://www.americaspg.com/journal/21/article/3470 https://www.americaspg.com/storage/51736513977.pdf