Inspired by the narrow Feshbach resonance in systems with the two-body interaction, we propose a two-channel model of three-component fermions with a three-body interaction that takes into account finite-range effects in low dimensions. Within this model, the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>p</a:mi></a:math>-wave Efimov-like effect in the four-body sector is predicted in fractional dimensions between <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>d</b:mi><b:mo>=</b:mo><b:mn>1</b:mn></b:mrow></b:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>d</c:mi><c:mo>=</c:mo><c:mn>2</c:mn></c:mrow></c:math>. The impact of the finite-range interaction on the formation of the four-body bound states in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>d</d:mi><d:mo>=</d:mo><d:mn>1</d:mn></d:mrow></d:math> is also discussed in detail. Published by the American Physical Society 2024
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