已知椭圆\(C _{1}\)：\( \dfrac {y^{2}}{a^{2}}+ \dfrac {x^{2}}{b^{2}}=1 (a > b > 0)\)的右顶点\(A(1 , 0)\)，过\(C _{1}\)的焦点且垂直长轴的弦长为\(1\)．
\((\)Ⅰ\()\)求椭圆\(C _{1}\)的方程；
\((\)Ⅱ\()\)设点\(P\)在抛物线\(C _{2}\)：\(y=x ^{2} +h(h∈R)\)上，\(C _{2}\)在点\(P\)处的切线与\(C _{1}\)交于点\(M\)，\(N.\)当线段\(AP\)的中点与\(MN\)的中点的横坐标相等时，求\(h\)的最小值．