So, when you count which number of a title a person is, you count from the start of that specific creation of the title. In this case, the Dukedom of Suffolk was granted three times, so the counting reset three times.

Firstly, you have William de la Pole, a member of an influential English family who had bankrolled large portions of the Hundred Year War, . William was a general in the latter stages of the war, and became an important member of Henry VI's court. By 1448 he was the principal power behind Henry VI and created himself Duke of Suffolk, having already been Earl of Suffolk, along with being appointed Lord Chamberlain. A dukedom was the highest title in English peerage at the time, generally reserved for the close royal family, and there were only 4 others in existence in 1448.

However, in 1492, William's grandson, Edmund de la Pole, the 3rd Duke of Suffolk, became the senior York claimant to the throne after the death of his older brother, and earlier his maternal uncle Richard III. Henry VII, who had ascended to the throne 7 years earlier, forced him to step down and renounce the Dukedom, which he did in 1493, but was allowed to keep the Earldom of Suffolk.

Charles Brandon, the son of Henry VII's standard bearer, and one of Henry VIII's close friends became the 1st Duke of Suffolk after the peerage was created again in 1514, partly for his services in fighting in France, and partly because he was to marry Henry's VIII's sister Mary. At this time there were only 3 other dukes in existence in England - it was extremely common for them to be created and renounced as people fell out of favour with the Crown.

Charles had four sons, and two of them succeeded him as Duke of Suffolk, but neither had sons of their own, so on the death of Charles Brandon, 3rd Duke of Suffolk in 1551, the peerage became extinct.

BUT, Charles had a lot of daughters, and the eldest, Frances Brandon, married Henry Grey, the 3rd Marquess of Dorset. When Henry VIII's son, Edward VI, died in 1553, the next in line to the throne was Mary I. The issue with her though, was that she was a catholic and seen by many as illegitimate due to Henry VIII having annulled his marriage to her mother Catherine of Aragon, and so unacceptable to a large portion of the English aristocracy. Because of this, before he had died Edward VI had named as his heir his cousin, the granddaughter of Mary Tudor, Lady Jane Grey. This didn't work, and for a number of reasons Mary successfully ascended to the throne, but in the nine days which Lady Jane Grey was Queen, she created her father as the 1st Duke of Suffolk, the same title as her grandfather and the 3rd creation of that title, before Mary executed him the year after for being complicit in an attempt to overthrow her. The Dukedom of Sussex hasn't been granted since.