This paper proposes a "minimal" fractional topological insulator (mFTI) in half-filled conjugate moiré Chern bands, motivated by experimental observations of a fractional topological insulator (FTI) at total filling factor ν_total = 3 in a transition metal dichalcogenide moiré system. The observed FTI is likely a topological state in a pair of half-filled conjugate Chern bands with Chern numbers C = ±1. The mFTI is characterized by a fully gapped topological order with 16 Abelian anyons (32 including electrons), a minimally-charged anyon with electric charge e*/2, and a fractional quantum spin-Hall conductivity σ^sh = 1/2. It is the unique topological state that respects time-reversal symmetry and has the smallest total quantum dimension among all possible topological orders with the same symmetry and Hall transport signals. The mFTI is also the common descendant of multiple valley-decoupled "product TOs" with larger quantum dimensions and can be viewed as the result of gauging multiple symmetry-protected topological states. The mFTI is classified by the stability of the gapless interfaces between different mFTIs. The paper also generalizes the construction of mFTI to a pair of conjugate 1/q-filled Chern bands and classifies all mFTIs via the stability of the gapless interfaces between them. The mFTI has a spin-Hall conductivity σ^sh = 1/2, consistent with experimental observations, and is protected by charge conservation and time-reversal symmetry even when S_z is not conserved. The mFTI is also shown to be the unique minimal topological order compatible with charge conservation, S_z conservation, time-reversal symmetry, and the desired Hall responses. The paper further discusses alternative constructions of the mFTI, including descending from larger topological orders and promoting SPT states. The mFTI is shown to be a symmetry-enriched topological order and can be constructed by gauging a part of the discrete symmetries of symmetry-protected topological states. The paper concludes with a classification of mFTIs with σ^sh = 1/q, showing that they are classified by the non-negative integer k in the decomposition q = 2^k p, where p is an odd integer.This paper proposes a "minimal" fractional topological insulator (mFTI) in half-filled conjugate moiré Chern bands, motivated by experimental observations of a fractional topological insulator (FTI) at total filling factor ν_total = 3 in a transition metal dichalcogenide moiré system. The observed FTI is likely a topological state in a pair of half-filled conjugate Chern bands with Chern numbers C = ±1. The mFTI is characterized by a fully gapped topological order with 16 Abelian anyons (32 including electrons), a minimally-charged anyon with electric charge e*/2, and a fractional quantum spin-Hall conductivity σ^sh = 1/2. It is the unique topological state that respects time-reversal symmetry and has the smallest total quantum dimension among all possible topological orders with the same symmetry and Hall transport signals. The mFTI is also the common descendant of multiple valley-decoupled "product TOs" with larger quantum dimensions and can be viewed as the result of gauging multiple symmetry-protected topological states. The mFTI is classified by the stability of the gapless interfaces between different mFTIs. The paper also generalizes the construction of mFTI to a pair of conjugate 1/q-filled Chern bands and classifies all mFTIs via the stability of the gapless interfaces between them. The mFTI has a spin-Hall conductivity σ^sh = 1/2, consistent with experimental observations, and is protected by charge conservation and time-reversal symmetry even when S_z is not conserved. The mFTI is also shown to be the unique minimal topological order compatible with charge conservation, S_z conservation, time-reversal symmetry, and the desired Hall responses. The paper further discusses alternative constructions of the mFTI, including descending from larger topological orders and promoting SPT states. The mFTI is shown to be a symmetry-enriched topological order and can be constructed by gauging a part of the discrete symmetries of symmetry-protected topological states. The paper concludes with a classification of mFTIs with σ^sh = 1/q, showing that they are classified by the non-negative integer k in the decomposition q = 2^k p, where p is an odd integer.