The growing integration of vehicle-to-infrastructure (V2I) communication within multitier heterogeneous networks (HetNets) introduces challenges in maintaining seamless connectivity and Quality of Service (QoS) for vehicular users. This paper introduces a modified Multicriteria and QoS-aware Vertical Handover Decision Algorithm (mV2I-MHA) tailored to address these challenges. By considering multiple criteria - such as packet loss ratio, cost, available bandwidth and packet latency - the proposed solution intelligently manages vertical handovers between different network tiers. Numerous Multi-Criteria Decision-Making (MCDM) techniques have been proposed to address the right target network selection aiming to reduce unnecessary handovers, incorrect network selections and the associated processing time. However, many of these solutions overlook the significance of varying criteria weights in vertical handover decisions made by their selection algorithms. Through comprehensive simulations and comparisons with existing techniques, the effectiveness of the proposed – in this paper - solution is demonstrated in enhancing handover success rate, reducing handover failure rate, minimizing latency, and overall elevating the QoS for V2I communication in multitier HetNets. MATLAB R2020a was utilized to simulate the work. Using packet latency and handover failure as the metrics for performance, the results were contrasted with those of an existing works in terms of handover failure rate and packet delay. The developed mV2I-MHA showed considerable percentage reductions of 10.5% and 23.9% in packet latency and handover failure rate, respectively.