Background The prevalence of smartphone usage is steadily rising, leading to the potential development of addiction due to problematic use. This study examined the relationship between smartphone addiction, self-perceived attention deficit and hyperactivity symptoms, and sleep quality among 443 university students at Bingöl University. Methods Participants completed several questionnaires, including the Smartphone Addiction Scale-Short Version (SAS-SV), the Pittsburgh Sleep Quality Index (PSQI), and the Adult ADHD Self-Report Scale (ASRS-v1.1). Results This study examined 443 participants, with a mean age of 20.97 ± 3.29, of whom 72.7% (n = 322) were female. The aim was to explore the relationship between smartphone usage patterns and sleep quality. Results showed that the majority of participants primarily used smartphones (94.8%, n = 420) for social media browsing (49.9%, n = 221). Factors such as smoking, preference for smartphone screens, and prolonged screen exposure significantly affected sleep quality. Smartphone addiction rates were notable, with 50.4% (n = 61) of males and 47.2% (n = 152) of females being affected, and this addiction was associated with poorer sleep quality. Correlations were found between age, sleep duration, and scores on smartphone addiction, sleep quality, and attention deficit scales. Linear regression analysis revealed that age, attention deficit scores, and sleep quality scores significantly influenced levels of smartphone addiction. Conclusions These findings contribute valuable insights into the impact of smartphone addiction on attention and sleep in university students.