NYC secedes from the US in early 1861

I could see the oligarchs once the coup was successful a business agreement would be signed making sure that the southern debts would be legally paid to New York City and perhaps an exclusive cotton deal would be sold or traded to new york city as a friendship token. If the city did not separate from the union at least the city would separate from the state. I do see that Mayor wood's power would increase and perhaps have near-dictatorial power with the Irish mob now under his thumb and the police now completely under his authority he still had the municipality police but not the metropolitan police. The mayor did a lot of great things for the city and the people did not forget his service to new york city.

Yes. 

Yes and during the Utah rebellion, they were not going to become an independent nation. However, Joseph Smith, when he was alive, was toying more with a thought of becoming a separate nation altogether. There will be people in New York City who said we refused to knowledge of the secession exist so we are part of New York states sell that doesn’t mean we want you to get ships and troops to bombard the city.

miletus12, the railways and rivers are under the rules of Governor Horacio Seymour and his pals such as Samuel J Tilden along with all businesses willing to resume normal relations with the mother city. I could even see the state Governor calling for state authority vessels to make sure Lincoln won't tamper or trespass under state territory whether it be by land or water. Furthermore, I could imagine that this coup would take the Brooklyn naval yard including the forts through indirect measures, and bribery before it attempts to seize the yard, head-on with Confederate agents.

I believe with enough time Horacio Seymour and the governor of Maryland would call for a league known as the central confederacy which was a collection of states that refused Lincoln's troops and declared themselves a league of armed neutrality, such as the war Kentucky did, and Missouri. If Lincoln dares violate this league of our neutrality, States will butterfly to the confederacy, at least many of them. New Jersey had the strongest amount of people who are interested in the central confederacy. Well, I’m not saying that New Jersey would succeed in it and possibly wouldn’t even join the central confederacy. It would hurt Lincoln.

Alright well unless the plot can materialize to take Brooklyn naval yard then nothing good for the CSA is going to come out of the session's movement.

John Alexander Kennedy Is the police superintendent so wood would have to convince his police to not act The superintendent knew of no existing plot

James Kerrigan was accused of being apart of the plot and later joined the union army whose regiment did not cheer for Lincoln

John Alexander Kennedy was stabbed at least 50 times during the riots. He was one tough hombre. The rioters regretted their mistake. 

James Kerrigan was a terrorist (Fennian) whose exploits (Nicaragua Filibuster, attempted invasion of Canada, and Alaska Expedition) made him no friends at all. He was cashiered out of the Union Army as "unfit" in 1862 and reverted to his usual profession of "scoundrel". He was not worth the minie ball to put him out of his misery.  

Summary: see MAP.

 

 In 1860, that geographic region is where 75% the cotton textile mills, 50% of the ordnance factories, 40% of the shipbuilding and 35% of the overseas trade of the United States occurred.  New York City was the major port that supported all of that effort. When the Confederates land blockaded the Mississippi River and cut off Ohio velley farm exports to Europe through New Orleans, that trade went by enlarged canal and railroad to the port of New York and increased tp near 50%.

European banks set up financial shop in New York City. American banks co-located next to them. 

Most immigrants recruited out of Europe to fill the ranks of the Union Army mid-war forward ($300 dollar men), landed in New York City and were press-ganged there.  Riker's Island became one of the four major Union army training camps for Irish-American and African-American citizens. 

90% of foreign loans to pay for the Union War effort was financed through the New York City banks.

More than 10% of the late war Union Army in the east were New Yorkers, the largest single recruited contingent. 

1/4 of the war built Union Navy was built in New York City, or about 100 ships of war. This is in addition to ships of trade. 

Most of the European steel (Krupp) used to repair and expand Union railroad trackline, came through the port of New York.  

I think that sums up New York City's functional impact.

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Politically the city was split between among a wealthy pro-Confederate pseudo-aristocracy, pro-Union manufactuerers and bankers, trades and business people, the Irish immigrant population and the old "Dutch". Like most seaport cities globally, this polyglot assemblage of humanity was too crowded, too dirty and too angry along ethnic and cultural lines to govern peacefully. The police force, answering to a politcal machine, called Tammany Hall, then as now, had a reputation as criminals, head knockers and strong arm bully boys.  That force was recruited from the same Irish immigrants as those who joined the Union Army and who lynched African Americans and rioted at Five Points in 1863. 

The Lincoln administration kept a garrison force locally of Union soldiers to "defend" the city from Confederates, but it was really there to keep an eye on the pseudo-Aristocrats, the Irish immigrants and the democratic party. After the 1863 riots, and a Confederate plot to sabotage the port, there were no illusions in Washington about the political class that governed or the powderkeg population that was New York City. In 1864, another Confederate plot to incite a rebellion, derange the national election inside the city and burn down the hotel district was foiled by the Tammany Hall political machine in a rare display of cooperation with Washington. The Confederates agents and sympathizers tried again (late September) and this time the Union Army intervened.         
 
New York City was as big a worry as any border state to the Lincoln administration, possibly as important as Maryland, or New Jersey.