The effects of dark matter annihilation on the evolution of the intergalactic medium (IGM) in the early Universe will be more important if the dark matter structure is more concentrated. Ultracompact minihaloes (UCMHs), which formed through dark matter accretion on to primordial black holes (PBHs) or an initial dark matter overdensity produced by a primordial density perturbation, provide a new type of compact dark matter structure to ionize and heat the IGM after matter-radiation equality z eq, which is much earlier than the formation of the first cosmological dark halo structure and later the first stars. We show that the dark matter annihilation density contributed by UCMHs can completely dominate over the homogeneous dark matter annihilation background, even for a tiny UCMH fraction f UCMH=ΩUCMH(z eq)/ΩDM≥ 10−15(1 +z)2(m χ c 2/100 GeV)−2/3 with a standard thermal-relic dark matter annihilation cross-section, and can provide a new gamma-ray background in the early Universe. UCMH annihilation becomes important to IGM evolution for approximately f UCMH > 10−6(m χ c 2/100 GeV). The IGM ionization fraction x ion and gas temperature T m can be increased from the recombination residual x ion∼ 10−4 and adiabatically cooling T m∝ (1 +z)2 in the absence of energy injection, to a maximum value of x ion∼ 0.1 and T m∼ 5000 K at z≥ 10 for the upper bound on UCMH abundance constrained by the cosmic microwave background optical depth. A small fraction of UCMHs are seeded by PBHs. The X-ray emission from gas accretion on to PBHs may totally dominate over dark matter annihilation, and may become the main cosmic ionization source for a PBH abundance f PBH=ΩPBH/ΩDM≫ 10−11 (10−12) with PBH mass M PBH∼ 10−6 M⊙ (102 M⊙). However, the constraints on gas accretion rate and X-ray absorption by baryon accumulation within UCMHs, together with accretion feedback, show that X-ray emission can only be a promising source much later than UCMH annihilation at z < z m≪ 1000, where z m depends on the PBH masses, their host UCMHs and the dark matter particles. Also, UCMH radiation including both annihilation and X-ray emission can significantly suppress the low-mass first baryonic structure formation. The effects of UCMH radiation on baryonic structure evolution are quite small as regards the gas temperature after virialization, but more significant in enhancing gas chemical quantities such as the ionization fraction and molecular hydrogen abundance in baryonic objects.