Does the new testament link Jesus to the manna in Exodus and how?

Yes. God used manna('bread from heaven"Psalm 105:40) to miraculously feed and sustain the Israelites in the wilderness (Exodus 16:15)(Numbers 11:7-9)

To see how Jesus is connected to this life saving food , his own Words can help us.

When asked by people what they had to do to please God, Jesus said:

"The work of God is this: to believe in the one he has sent."

So they asked him, "What sign then will you give that we may see it and believe you? What will you do? Our ancestors ate the manna in the wilderness; as it is written: 'He gave them bread from heaven to eat.'"(Nehemiah 9:15)

Jesus said to them, "Very truly I tell you, it is not Moses who has given you the bread from heaven, but it is my Father who gives you the true bread from heaven. For the bread of God is the bread that comes down from heaven and gives life to the world.......Then Jesus declared, "I am the bread of life. Whoever comes to me will never go hungry, and whoever believes in me will never be thirsty. But as I told you, you have seen me and still you do not believe. All those the Father gives me will come to me, and whoever comes to me I will never drive away. For I have come down from heaven not to do my will but to do the will of him who sent me. And this is the will of him who sent me, that I shall lose none of all those he has given me, but raise them up at the last day. For my Father's will is that everyone who looks to the Son and believes in him shall have eternal life, and I will raise them up at the last day...."(John 6:28-40 NIV)

"I am the bread of life. YOUR forefathers ate the manna in the wilderness and yet died. This is the bread that comes down from heaven, so that anyone may eat of it and not die. I am the living bread that came down from heaven; if anyone eats of this bread he will live forever; and, for a fact, the bread that I shall give is my flesh in behalf of the life of the world."(John 6:48-58 NIV)(1 Corinthians 10:1-4)