Abstract: The first search for the doubly heavy Omega(0)(bc) baryon and a search for the Xi(0)(bc) baryon are performed using collision data collected via the experiment from 2016 to 2018 at a centre-of-mass energy of, corresponding to an integrated luminosity of 5.2 fb(-1). The baryons are reconstructed via their decays to Lambda(+)(-)(c)(pi) and Xi(+)(c)pi(-). No significant excess is found for invariant masses between 6700 and 7300 MeV/c(2), in a rapidity range from 2.0 to 4.5 and a transverse momentum range from 2 to 20 MeV/c. Upper limits are set on the ratio of the Omega(0)(bc) and Xi(0)(bc) production cross-section times the branching fraction to Lambda(+)(c)pi(-)(Xi(+)(c)pi(-)) relative to that of the Lambda(0)(b)(Xi(0)(b)) baryon, for different lifetime hypotheses, at 95% confidence level. The upper limits range from 0.5x10(-4) to 2.5x10(-4) for the Omega(0)(bc) -> Lambda(+)(c)pi(-) (Xi(0)(bc) -> Lambda(+)(c)pi(-)) decay, pending on the considered mass and lifetime of the Omega(0)(bc) (Xi(0)(bc)) baryon.