Face recognition for infants and toddlers presents unique challenges due to rapid facial morphology changes, high inter-class similarity, and limited dataset availability. This study evaluates the performance of four deep learning-based face recognition models FaceNet, ArcFace, MagFace, and CosFace on a newly developed longitudinal dataset collected over a 24 month period in seven sessions involving children aged 0 to 3 years. Our analysis examines recognition accuracy across developmental stages, showing that the True Accept Rate (TAR) is only 30.7% at 0.1% False Accept Rate (FAR) for infants aged 0 to 6 months, due to unstable facial features. Performance improves significantly in older children, reaching 64.7% TAR at 0.1% FAR in the 2.5 to 3 year age group. We also evaluate verification performance over different time intervals, revealing that shorter time gaps result in higher accuracy due to reduced embedding drift. To mitigate this drift, we apply a Domain Adversarial Neural Network (DANN) approach that improves TAR by over 12%, yielding features that are more temporally stable and generalizable. These findings are critical for building biometric systems that function reliably over time in smart city applications such as public healthcare, child safety, and digital identity services. The challenges observed in early age groups highlight the importance of future research on privacy preserving biometric authentication systems that can address temporal variability, particularly in secure and regulated urban environments where child verification is essential.