  By using a class of `anyon like' representations of permutation algebra,
which pick up nontrivial phase factors while interchanging the spins of two
lattice sites, we construct some integrable variants of $SU(M)$ Haldane-Shastry
(HS) spin chain. Lax pairs and conserved quantities for these spin chains are
also found and it is established that these models exhibit multi-parameter
deformed or nonstandard variants of $Y(gl_M)$ Yangian symmetry. Moreover, by
projecting the eigenstates of Dunkl operators in a suitable way, we derive a
class of exact eigenfunctions for such HS like spin chain and subsequently
conjecture that these exact eigenfunctions would lead to the highest weight
states associated with a multi-parameter deformed or nonstandard variant of
$Y(gl_M)$ Yangian algebra. By using this conjecture, and acting descendent
operator on the highest weight states associated with a nonstandard $Y(gl_2)$
Yangian algebra, we are able to find out the complete set of eigenvalues and
eigenfunctions for the related HS like spin-${1\over 2}$ chain. It turns out
that some additional energy levels, which are forbidden due to a selection rule
in the case of SU(2) HS model, interestingly appear in the spectrum of above
mentioned HS like spin chain having nonstandard $Y(gl_2)$ Yangian symmetry.
