  The future long baseline experiments such as DUNE and T2HKK have promising
prospects to determine the neutrino mass hierarchy and measuring standard $CP$
phase $\delta$. However, presence of possible non-standard interactions of
neutrinos with matter may intricate this picture and is the subject matter of
the present work. We have studied the standard parameter degeneracies in
presence of non-standard interactions(NSI) with DUNE and T2HKK experiments. We
examine the mass hierarchy degeneracy assuming (i) all NSI parameters to be
non-zero and (ii) one NSI parameter($\epsilon_{e\mu}$) and its corresponding
$CP$ phase($\delta_{e\mu}$) to be non-zero. We find that the later case is more
appropriate to resolve mass hierarchy degeneracy with DUNE and T2HKK
experiments due to relatively small uncertainties emanating from the NSI
sector. We have, also, investigated the octant degeneracy with
neutrino($\nu_{\mu}\rightarrow\nu_{e}$) and
antineutrino($\bar{\nu}_{\mu}\rightarrow\bar{\nu}_{e}$) mode separately. We
find that to resolve this degeneracy the long baseline experiment with
combination of neutrino and antineutrino mode is essential. Furthermore, we
have considered DUNE in conjunction with T2HKK experiment to study $CP$ phase
degeneracy due to standard($\delta$) and non-standard($\delta_{e\mu}$) $CP$
phases. We find that DUNE and T2HKK, in conjunction, has more sensitivity for
$CP$ violation effects(10$\sigma$ for true NH and 8.2$\sigma$ for true IH).
