With the increasing deployment of additively manufactured Ti-6Al-4V in aerospace and other high-performance structural applications, reliable prediction of fatigue life under complex multiaxial loading has become essential for safe design and lifecycle management. However, conventional data-driven approaches often lack predictive accuracy and physical consistency on small datasets and non-proportional multiaxial stress states, limiting their generalizability and interpretability. To address these limitations, this work computes the Mises equivalent stress directly from experimental loading histories and incorporates a Basquin-model-based theoretical fatigue life as prior physics knowledge. Building on this prior, we propose a residual connection-based physics-informed neural network (PI-Res) that learns only the datadriven residual relative to the theoretical life, thereby merging mechanistic fidelity with statistical adaptability. Using laser powder bed fusion (L-PBF) Ti-6Al-4V as the case material, we conduct a systematic comparison against representative purely data-driven baselines—artificial neural networks, random forests, and support vector regression—as well as three canonical data-physics fusion strategies: physics-informed feature engineering, physics-informed loss functions, and physics-informed residual connections. Across multiaxial loading scenarios and distinct life regimes, the PI-Res framework consistently demonstrates superior predictive accuracy alongside stronger adherence to physical trends implied by the stress-life relationship. Moreover, by anchoring the learning process to a mechanistic prior and delegating only the unexplained variance to the network, PI-Res improves robustness under data scarcity and enhances interpretability of model behavior. These findings indicate that residual-style injection of domain knowledge offers a principled pathway to reconcile small-sample constraints with mechanistic coherence in fatigue modeling. Practically, the proposed approach provides a reliable tool to support fatigue life assessment, design margins, and maintenance scheduling for additively manufactured components. Theoretically, it illustrates a transferable physics-data fusion paradigm that can be extended to other material systems and generalized multiaxial fatigue problems where integrating prior physics with flexible learners is crucial.