Secessionist such as Alexander Hamilton handy worried that the Republican Party would pass laws that

will exclude slavery from all the territories,

Explanation:

Alexander Hamilton Handy was a secessionist who served as a Chief Justice in Mississippi. Secessionist was a belief in which they believed that the slave states should not be permitted in Union.

At this time, the Republican Party was formed. With the formation of this political party, secessionists such as Alexander Hamilton Handy feared that this Republican Party would pass laws that would exclude slavery from all the territories. This abolition, he believed would be a threat to the safety of the Southerners.

Thus the correct answer is that they would exclude slavery from all the territories.