This paper investigates the nuanced dynamics of misinformation spreading in social networks, with a specific focus on the propagation of targeted misinformation within a closed homogeneous minority community characterized by a small world network. In contrast to epidemic spreading, misinformation can be tailor-made to target specific groups, amplifying its impact. The study introduces an I2S2R model, distinguishing between targeted and non-targeted information propagation structures. To emulate a community structure, the model considers a high clustering coefficient. The basic reproduction number is considered the outcome variable to assess the influence of the community structure on misinformation propagation. Additionally, the model explores the interplay between two types of misinformation over a specified period. This research contributes to understanding the complex relationship between community structures and targeted misinformation dynamics, offering an important overview of the potential vulnerabilities and impacts within minority communities.