Existing low-resource in-context learning-based knowledge graph question answering (KGQA) methods rely heavily on large language models (LLMs) to convert the natural language question into its corresponding logical form (LF), such as SPARQL, KoPL, etc. Recently, a few alignment techniques have been introduced that enable instruction-based fine-tuning of language models. They provide explicit negative signals and comparative objectives to learn how to avoid negative signals using preference optimization methods. Exploring such fine-tuning techniques with LLMs becomes very challenging due to the high computational resource requirements associated with them. Due to this, the focus has been shifted towards Small Language Models (SLMs), which offer advantages such as ease of (i) deployment for practical applications and (ii) instruction fine-tuning for specialized tasks. Motivated by this, in this work, we propose PO-KGQA: An SLM-based preference optimization framework for the complex KGQA task in a low-resource setting. Our extensive experiments demonstrate how PO-KGQA outperforms other fine-tuning alignment techniques on complex benchmarks such as KQA Pro by approximately 9% (avg).