  By using an extended slave-boson method, we draw a global phase diagram
summarizing both magnetic phases and paramagnetic (PM) topological insulating
phases (TI$_s$) in three-dimensional topological Kondo insulator (TKI). By
including electron hopping (EH) up to third neighbor, we identify four strong
topological insulating (STI) phases and two weak topological insulating (WTI)
phases, then the PM phase diagrams characterizing topological transitions
between these TI$_s$ are depicted as functions of EH, $f$-electron energy level
and hybridization constant. We also find an insulator-metal transition from a
STI phase which has surface Fermi rings and spin textures in qualitative
agreement to TKI candidate SmB$_6$. In weak hybridization regime,
antiferromagnetic (AF) order naturally arises in the phase diagrams, and
depending on how the magnetic boundary crosses the PM topological transition
lines, AF phases are classified into AF topological insulator (AFTI) and
non-topological AF insulator (nAFI), according to their $\mathcal{Z}_2$
indices. In two small regions of parameter space, two distinct topological
transition processes between AF phases occur, leading to two types of AFTI,
showing distinguishable surface dispersions around their Dirac points.
